The Alexander is a great choice and comes with everything except a wheel. As regards moving them, I am on the cautious side and allow for a transition. Our last hamster completely freaked out when I moved him, for about 10 days and would sit and shake - it was very upsetting, we nearly moved him back again. It depends on the hamster to some degree, their personalities differ, but I did find doing a transition worked a treat when upgrading him again (yes many people end up having to upgrade as pet shops sell such small cages!).
Doing it the transition way, I filled the new cage base with substrate and put a couple of toys in, and put our hamster in one evening to explore it. He loved it for about 15 minutes and then wanted to come out, so I put him back in his old cage. Half an hour later he had this look as if wanting to come out again, so I put him back in the new cage and he stayed in it for a long time, exploring and sitting and looking happy (in a hamster way), then went back to his old cage for the night.
Next day I popped him in his pet carrier to sleep for the afternoon, and took all the old substrate from his old cage and spread on top of the substrate already in the new cage (when you move to a larger cage you don't have enough from the old cage) and moved his toys and house and wheel across and tried to put things in similar positions. Moved him in that night and he settled straight away.
It's up to you. Because I had a slightly stressful experience of a cold turkey upgrade, I prefer to do the transition way. I think it means that when they move in they have already scented the cage and it seems more familiar straight away.
Some people just put the whole of the existing cage base, already set up, inside the new cage and let the hamster explore out from it, when moving them (depending on the size of the old cage base). And then remove it, leaving the contents, in a couple of weeks for a minor clean time.
Wheel - I like the 12" Silent Runner wheel - best wheel I've had. It is silent, it spins very well (spins better than the wodent wheel) and is light and easy for them to run in. Also the holes are big enough to just give it a quick wipe without removing it from the cage, as and when needed. It isn't cheap but I've had it over a year with no issues. Our first wood wheel was broken after 6 months. It works particularly well with the bar mounting plates as you can put it at the height you want and it doesn't interfere with the substrate in the cage base that way. Either way it's nice and stable.
The wodent wheel is good too, but I think the Alexander is a difficult cage to attach it to due to the sloping roof and it could end up too high as well.
I wouldn't put the cage in our 8 year old's bedroom (9 now) but it depends on the 8 year old. It's easy to forget to close a cage door and the hamster escape. I would wait until the hamster is fully tame and easily handleable, and until your daughter has been used to handling him with some supervision and knows how to hold him without squeezing etc. Yes handwashing is needed first especially if just had food
Hamsters don't like a hand in the cage. It's better if they are handled out of the cage. They come to the door if they want to come out. But as you say, they often don't wake up very early.
With children you can get into a routine of gently waking the hamster around 6pm or 7pm each night, when putting food out, making a bit of noise about it, eg food rattling in bowl or cage door opening with a bit of noise. This is ok if you get them into the routine of it. I have to do it anyway now as our hamster started getting up later and later. They are a bit dopey when woken and will bite if a hand wakes them up sometimes. So give her a few minutes to come round. I used to have to get ours out in a tube with some food in the end, putting the tube over the house door and the food in the far end and they walk in, then lift the tube out with your hands over either end. If you need to transport the hamster somewhere to let them out of the tube, then I used to put one end of the tube in the hamster ball after lifting ours out and let the hamster walk into the ball - then carry them in the ball to where you're going to let them out that is hamsterproof!
It's great that she runs all over you on the sofa. As Cypher says, you may need to leave her alone again for 2 to 3 days to settle in after the cage move and then start again with handling and taming. Or she may settle in quicker and come to the cage door wanting to come out. Talking to them through the cage bars can help them familiarise with you while waiting 2 or 3 days.
The Alexander comes with a lovely big long house built into the base, which hammies seem to really like as it has two entrances and is big enough to build a big nest in. It's also big enough to have a bathroom at one end, so if she starts peeing at one end of the house, you could put a litter tray in there and she will most likely use it. They do usually use a litter tray, but only if you put it in the area they have chosen as a toilet! That way you can just empty the litter tray every 5 days or so and cleaning won't need to be done so often.
General advice is not to do any clean outs at all for the first two weeks, while the hammy settles in as it removes all their scent marking. They scent mark to find their way around because they don't see well at all. So if everything is cleaned out in one go, they are lost and it can be stressful. You can "spot clean" mostly. ie take a handful of soiled or wet substrate out and replace with a handful of clean and mix it in. They are clean little things, wash a lot and will use a litter tray. I find if the litter tray is used the rest of the cage stays clean and doesn't smell. Their poops aren't an issue - they are like little hard black seeds, and they will sometimes eat them, which is normal, to get extra vitamins. They also sometimes hoard them in case food is ever in short supply!
I tend to spot clean, and just change the substrate every 2 to 3 months and wipe out the cage base with a damp cloth at that time, or use washing up liquid in water to clean it. Disinfectant isn't necessary unless there has been illness or disease, and then only use a petsafe one like the Johnsons one for hamsters.
And clean the toys/wheel at a different week to doing the substrate so that way something always smells familiar. Some hamsters pee in their wheels a lot, some never. I rarely have to take the wheel out to clean it completely, but occasionally need to give it a wipe inside, and save washing it completely for when it really needs it.
Toys tend not to need cleaning that often unless they get pee'd on or something, although a wipe is needed now and then or they gather dust!
The Alexander has such a lovely large base that you can fit a lot of substrate in, and that means it needs cleaning less as well as most if it will stay dry. It will take quite a lot the first time you fill it, and it needs to be deep enough to cushion any falls. Plus they like digging. Three to four inches is the minimum recommended but if you fill the base to just below the edge it means the bottom half tends to stay clean and you only need to replace the top half each time and mix it in. Plus it gives the hamster something to dig in and they like pushing it around and building mountains sometimes too.
A lot of people like using Fitch for substrate - you buy it in bulk (either 10kg or 20kg) and it lasts for ages. It's made from recycled food grade paper and is dust free. Hammies like it too because it's nice and soft. They will sometimes add it to their nest. The safest nesting material is torn up strips of plain white toilet paper. If the pet shop have sold you any fluffy bedding, then that needs removing and binning as it's dangerous! Paper is safest for nesting. They pouch nesting material sometimes.
Try not to remove the hammies nest (she will build a new one when you move her although you could move her old one over as well, but she will probably just build a new one where she wants). Unless it is pee'd in, and then try and leave a dry bit behind and put new nesting material out in a heap somewhere in the cage (not in her house) and she will take what she wants and rebuild it. That is their number one most important thing, their nest and they can get upset if it is removed regularly. There are probably three most important things to them! Their nest, their hoard and their wheel. If you need to remove any hoard because it is wet or pee'd in then always replace it with new food in exactly the same place. Dry hoard can be left for quite some time.
As Cypher says, it can be an idea to move the old house in. I think if it is a little plastic one with a filled in bottom, I wouldn't move it with her and would just put her nest in the cage. She will probably then nest in the big house in the Alexander. You don't want her continuing to nest in a little plastic house as it will get smelly and need cleaning out often. A house is best open underneath and on top of the substrate, so they can bury hoards under their nest and snuggle down and keep their nest clean themselves. The big house in the Alexander goes right down to the cage base, so putting some substrate inside it helps (leaving enough head room!).
I think the bar chewing will stop when she is moved and has more space. Plus the 7mm bars are harder to chew. It is an indication that something isn't right, or they are trying to tell you something usually. Although it can become a habit. A change will probably stop it. Sometimes they do it because - the water bottle is empty, the wheel is stuck, or some other problem, rather than as a habit, so if they do start acting frantic or chewing the bars when they don't normally, just check everything is ok.
It's common for them to chew bars in cages that are too small and that's probably the issue. So an upgrade sounds good.
Adding hidey places as toys goes down well. A tissue box eg.