Agree with cypher. Putting a treat in the wheel sometimes encourages them to use it. He might just not feel energetic enough yet, but if he goes in the wheel to get the treat (maybe a tiny piece of cucumber) he might run in it. If he doesn't he's probably not ready yet.
I should go easy on the lettuce! They do love eating lettuce and cabbage and I used to give it to our hamster, but apparently it's not that good for them! Safe veg include broccoli, carrot, cucumber (not too often), peas, cauliflower. I tend to rotate those. The lettuce won't have done him any harm and I can't remember why they're not supposed to have it very much. I put a bit of raw veg out each day - just a very small piece like a cubed centimetre size.
I also used to wonder about the scent thing, thinking he might associate my scent with the person who messed up his nest! I think they are aware of that, but also it doesn't quite work like that, in that they know your scent is something familiar and is not a predator - it would freak him out more if a strange person had messed with his nest!
With the tissue thing, I use about four 'sections' of white toilet roll paper, leave them under your clothing near your skin for an hour or so, then tear them into strips and put the strips of paper in. When he pouches it to add to his nest, his nest will have your scent and he will get used to you being a good thing and not a predator.
1) Yes it probably isn't good to chase him round the cage - it's his territory - better if he hops into something you can lift out, like a cup or a small hamster ball (hamster balls aren't recommended for dwarf hamsters but I find they quite good for transporting a hamster safely!) Or a tube as Cypher says. A kitchen roll tube is good because it's quite long - you can put a small treat at one end (eg a tiny piece of cheese) and he should just crawl in and you can lift the tube out, but be careful to have your hand over each end of the tube when you lift him out or they can jump or fall out. I get the impression you are a bit worried about him biting - he will pick up on this and if you feel jumpy he will get more jumpy! So just relax and think - if he does bite me while my hand is over the tube I'll just expect it - and it probably won't happen, which will build your confidence at doing this. I think a ball or cup is easier to get them out though although you still need one hand over the top.
He is clearly feeling nervy or shy if he has built himself a tunnel system area to be out of sight. The tube might be best for now as it's easier to keep him in than a cup and assume you don't have a ball. Before Charlie was tame I would get him into the tube in the cage, with the other end of the tube in the ball and another treat in the ball, so he would walk right through into the ball, and then pop the lid on before lifting him out. Out of the cage they are more relaxed and less territorial. Or get him out in the tube with my hands over either end and then let him walk into the ball with just one end of the tube covered. Once in the ball I could take it wherever I wanted to let him out that was safe. Initially that was the bathtub! As he would try and leap if I put him on the sofa, although eventually we got to blocking off the edges of the sofa with a blanket so we could catch him before he got too far. But if he is zippy and hard to catch, then putting him in something enclosed like a bathtub would be good for taming and handling gradually. If you don't have a bathtub then a very large cardboard box would do. Put a couple of toys in there (his wheel maybe? He might get used to it out of the cage more), a cup and scatter/ hide some food so he can search it out (which will distract him from being nervy! Some people make like a Christmas cracker toy - put food in a toilet roll, roll a piece of paper round it and twist the ends like a cracker, then they have to work out how to get into it to get the food - which is a good game!
To get him a bit tamer he needs to be out of his cage, in a safe place he can't escape from. Then before trying to pick him up, just try stroking him gently on the back with one finger while he's in the bathtub or box - if you're worried he might turn on you and bite (ours used to jerk his head round and 'threaten' but never actually bit!) then start the stroking with something like a toothbrush, and gently stroke his back with that, that way the toothbrush gets a nip rather than you. When he accepts that, try stroking him with one finger, just a second or two, then leave it for a bit, then again. This might take 2 or 3 sessions. Once our hamster got used to being touched without leaping or jerking round, we moved onto slipping a hand underneath him and slightly cupping him and just lifting him a centimetre or so and letting him walk off again. Leave it a bit then do this again. After a few times of this we could pick him up easily and he didn't try to run off. Ours is a Syrian though so a bit different, but the same principles apply really. It might come quicker than you think, seeing the photos of him sitting in your hand. Sometimes they just want their own space though. But a bit of handling each day gets them more tame - if it's left for a week they can revert a bit.
Because he is in a tank, your hand will be coming from above and chasing him round the cage
which might seem like a predator, even if he does recognise your smell. A tube can be on a kind of level and you can pick it up when he's in it and can't see (although I tended to keep hold of the far end). A ball they can just hop into and it's easier to lift out. That's covered number 2 as well.
3) They often eat at night when you can't see, and will tend to pouch food and take it to the nest and eat it there. I always put my finger under the water bottle spout and tap it each day and make sure it gets wet, to make sure water is coming out ok. If it is, your ham will find the water and try and get it out by licking the end of the spout which will let more out. They do seem to know how to use them, although I had a Ferplast sippy bottle once and charlie didn't work that one out (completely vertical and a sticky out thing instead of a ball in a spout). Just make sure he can reach it ok. You can make a bottle stand out of a plastic bottle with the top cut off and a hole in the side - it holds the bottle in place with the spout sticking through the hole, if it would be easier to have it in the cage rather than attached to the side, if that is an issue, but best not to change too many things in the cage too often as this does freak them out.
It's lovely to see how much better he is - you've done an amazing job. it might be time for some deeper substrate/litter now instead of the towels - he might dig tunnels in that instead of making tunnels out of the cardboard tubes and I always think they look happy playing in deep soft substrate. Kaytee clean n cosy is supposed to be very good in the US (less dusty than Carefresh). Fitch is a good one too but that's Uk only. He'll probably hide in that too so you'll need to tempt him into something with a treat. Sometimes they are more nervy if they feel there is a lot of open space above them (hence liking a hide or house), so deeper substrate will help him feel more secure. Our Syrian likes sitting in his sand bath which is like a little round ceramic thing. Not sure if you have a sand bath, but it sounds like he could do with one now. Any kind of plastic or ceramic dish would do if the sides are low enough or there's a ladder or bridge up to it and as long as it is Chinchilla bathing sand (and not 'dust'). Dwarf hamsters love their sand baths and this will help him feel more at home in his cage too. I think that's covered 4 as well. Any kind of little hidey place with a roof on so they can nip from one safe roof to another
Small salt pigs can make a good sand bath or you might find something similar in your cupboard! You can buy these ones but any dish will do (they look a bit like small salt pigs but are cheaper).
Amazon.com : Kaytee Ceramic Critter Bath, Small, Colors Vary : Pet Grooming Supplies : Pet Supplies
Some people use a glass cookie jar but that might take up too much space in your tank.
http://www.amazon.com/Anchor-Hocking...S0EN8SJFS29VFG
Otherwise a plastic ice cream tub would do as well.
This is the 'safe' sand - he might use the sand bath as a toilet too, so then his nest would stay dry and you wouldn't have to disturb it too much.
http://www.amazon.com/SUPREME-PET-FO...hinchilla+sand
Washing and grooming a lot is what hamsters do - sometimes they do it more when they're a bit anxious but this is quite normal. The fact that he can do it while sitting on your hand suggests he is quite comfortable doing it there. It's partly a nervy thing but they are also very clean. He might do it less if he had a sand bath to throw himself around in and roll in.
6) Dwarf hamsters can have a reputation for being a bit nippy sometimes, but not all of them - it depends on the hamster. If he hasn't bitten you yet I should think he'll be fine. If he does it will usually be out of fear or because you smell of food! If you wash your hands before handling him he won't try to taste you! I know that sounds weird - on the one hand you want them to recognise your familiar scent, but then wash your hands - they can still smell you through the soap though I reckon, or smell you past your hands. I saw one good tip recently to not use those liquid soaps with things like honey and oatmeal in - just some kind of plain standard soap - I sometimes just use washing up liquid or unscented soap, but any soap is ok as long it's not food scented!
Answered 7 already. But what makes them wheel is a combination of things. Mainly exercise, plus it can be fun and they sometimes do it a lot when they are scared and running away from something or a bit stressed, so too much isn't good either but that's usually a temporary blip. What wheel do you have and what size is it? The small 6.5" silent spinners are the size people usually get for small dwarf hamsters and a lot of people have been having problems with those being stiff and not spinning since a manufacturing change - so if it won't spin easily he might not be trying any more. So check it spins freely. Anything up to an 8" wheel should be fine but a smaller one would be easier for him. There are 4" silent spinners though and these are too small for any hamster, so if it's that small he probably won't use it - it can hurt their backs if it's too small. 6.5 to 8" diameter should be fine.
Sorry I can't remember if you are in the US or not - I seem to remember you are? Hence mentioning Kaytee Clean n Cozy being a good substrate. It's also nice and soft - he will love it I'm sure.
It is so lovely that you have brought him back to health. I'm not an expert in dwarf hamsters, but I believe Robos are very zippy and people find them very entertaining, but not necessarily keen on too much human contact (they probably don't like sitting still long enough!). I get the impression they are either very active or asleep with not a lot in between! Must be strange though when he was not active due to being so poorly.
From what I have learned, "enrichment" is the key to normal behaviours and a happy hamster.
Enrichment includes a number of things - substrate to dig in, variety in the cage and toys/hides, things to go under and over, sand bath, things to chew on like chew sticks or toys, the wheel, a safe house/hide and good floor space. A German scientific study said that digging tunnels in deep substrate reduced stress levels hugely (can't remember the statistics, sorry).
So maybe it's time to add a few more things to his tank. Just gradually, a couple of things at a time maybe. I'd try putting some deep substrate in and a sand bath and maybe a toilet roll toy. There's a video here from Erin's Hamsters showing ten toys you can make out of toilet roll tubes
https://www.youtube.com/watch?v=NuPeyD6w-CI
She also has a good video on cage cleaning which helped me a lot because our hamster was very nervy for the first few months and hated anything being done to his cage at all.
https://www.youtube.com/watch?v=5jVnEjrXbww
I made a little video on ideas for toys for Syrian hamsters recently - not 100% relevant as Syrians are much bigger, but it might give you some ideas! They don't all have to cost money, you can improvise.
https://www.youtube.com/watch?v=nAZYfMZEzeY
Having said all that, safety is important too - no drops from a height or they can get injured. I also think, as others have said, that the smell of cat will probably stress him out as he will smell predator! The fact that he is in a tank will help and assume you have a lid for that (I think you can buy lids or tank toppers in the US for the standard sized tanks, or make one out of mesh. Even so I guess you have it placed out of reach of the cats.
Maybe try and attract the cats elsewhere in the house with a catnip toy or something - or put a bolt on the door!
Looking forward to hearing more about this lovely little guy - I want him! Sadly I'm too far away. Talking to them does make a difference as others say - they pick up on tone of voice and the familiarity of it. But he is a robo and his mission in life is to be very fast, eat, hoard and nest - but they can bond with a human as well - to some degree. It would be nice for you if he was tamer, and also for any prospective new owner.
I think the main issue at the moment, is somewhere you can handle him out of the cage, safely. Cats can be very clever at getting at small rodents and I am sure he feels anxious about this out of the cage - he will sense it. Is there somewhere you can take him for out of cage time where you can be on your own with him, without a lot of noise, like tv and kettles boiling, and where the cats can't get in. Maybe the bedroom with the 'taming box' on the bed and then lift him out onto the bed a bit sometimes (providing you can block the edges off so he can't jump off) - or a makeshift playpen on top of the bed.
Is he on dwarf hamster mix now? Scatter feeding can give them pleasure too - ie scattering a bit of food in the cage, so they can hunt it down - I still put some in the food bowl as well in case ours gets dozy and doesn't find enough scattered food lol.