Hello and welcome. It sounds like you've got her a great set-up! There have been issues with the 12" Silent Spinner not running well - for a couple of years now, since a manufacturing change. ie stiff to spin and hard work for the hamster to push. Sounds like she has been managing it until now. You can check if it's working well by pushing it with your hand and see if it spins freely or just moves a few mm! If it isn't free spinning I would take it back (even though used) and get a refund and say it doesn't spin properly. There is a totally silent wheel - the 12" Silent "Runner" which spins really well.
The first thing I will say is - your hamster is a baby! A tiny scaredy baby - a toddler! It can help to remember that rather than think of them as a bitey animal.
So it is normal at first for hamster and owner to be a bit skittish with each other. And it takes a while to stop being jumpy - if you get jumpy, she picks that up and gets jumpy too! I had all of this when we got a hamster, and it is just a confidence building exercise and a bit of time and patience and getting to know each other.
At the moment you are "strangers". Suspiciously eyeing each other! Hamsters can get a bit upset by people "doing things" in their cage or messing with their wheel! When I say upset, I don't mean angry. It is their territory and they are prey animals so she will be more scared than you
Main thing I would say is - I have never yet been bitten by a hamster and we have had three (currently have two). They bite for two reasons - either because they are scared (some people hold them too tight or high up) or because they are in pain. There is a third time and that is if you stick your hand inside their house when they're asleep and they wake up startled. I think you might also lash out if someone startled you awake who wasn't supposed to be there!
What they can do, before they are tame, is run at your hand to see you off - because if they see your hand doing a lot of messing in their cage they feel scared by the invader! That should be less of an issue in your case as it's a good sized cage and is more associated with cage rage.
What I will say is - when a bond forms you can have really good little conversations - they communicate with facial expressions (disgust! happy, look at me - that kind of thing).
It is nerve-wracking for any new owner to handle a hamster, because they are not yet hand tame or learned to trust you. And the best way to start with is having them out of the cage - either in the dry bathtub (if you have one), or if not, a playpen area.
If you have a hamster ball, you can put a treat in it, lower it in the cage and put it near her house and she should walk in - then pop the lid on. If you feel nervous doing this, then wear gloves. The nerves soon wear off the more you get in the habit of these things.
You then lift the hamster ball out and carefully carry it to the bathtub or taming area (bathtub is ideal as not too big and they can't escape), set the ball down and take the lid off with the opening on one side so she can just walk out. I used to leave the ball in the bath, propped on its side, as our hammy would jump back in when he'd had enough.
It's a good idea to have a few toys in there - a cardboard tunnel and a mug on its side would do. They then tend to just slither up and down the side of the bath trying to escape! But will wander off and explore the tunnel etc now and then. Hiding or scattering a few treats attracts them to explore.
So to begin taming, it is not scary or difficult. You can wear gloves. And just gently stroke her on the back with one finger, just once, while she is running up and down the side of the bathtub. She may jerk around as if to bite your finger but it will probably just be a jerk to see you off.
Wait a while, then do it again. Maybe do this 2 or 3 times on the first session.
Two or three days later repeat the process. And she will soon get used to a stroke on the back with one finger and stop jerking around and accept the stroke. This is a big turning point. It means she trusts your touch and trusts it isn't going to hurt her (she is probably more scared of being hurt than you!).
So you then move on to letting her walk over your hand. Put the back of your hand flat on the bathtub just in front of her and let her walk over the palm of your hand, but don't try to pick her up. By then you may be feeling confident enough to do it without gloves. Do this a couple of times.
Next session 2 or 3 days later. Do this again, but this time, raise your hand very slightly, maybe 1cm, after she walks onto it, but still let her walk off. Then raise it a little bit higher when she walks onto it again (you'll need to place your hand in her path) and let her walk off again.
From there it should be easy to actually lift her and hold her and let her walk between both hands, without her "pinging" (ie wriggling and leaping away) and at that point she trusts you and is hand tame.
From then on you should always be able to handle her easily, pick her up, stroke her, etc. Bearing in mind they often don't like to sit still for more than a few minutes for a stroke and like to be off exploring.
But - all this is good out of the cage. Inside the cage is their territory and they don't like being handled inside the cage - it's like - I didn't invite you in here and I'm doing my own thing.
So I always either let our hamster walk into something and lift him out, or wait until he is telling me he wants to come out (with a cage they can come to the door and pester you - with a tank I am sure she will let you know somehow that she wants to come out).
They really are such funny friendly little things and so vulnerable. Easily injured, hence their fear until they trust you. But when they do trust you and you can enjoy time out of the cage with them, it can bring a lot of joy and laughter at their funny behaviour and antics.
I've added a couple of videos of when our current Syrian was a baby (baby hamsters can be very fast and a bit nervous) during playpen time. Just to give you an idea of how they are much more interested in food and having fun than they are of biting anyone!
The only other point to make is, if your hands smell of food, they may try and nibble to test and see if you're edible - that doesn't hurt - and is easily avoided by always washing your hands before handling in some plain kind of soap (not soap with honey or flower scents!).
Our hamster eats tiny pumpkin seeds from the palm of my hands and has never once nipped or accidentally bitten - he is very careful and uses his tongue mostly! They are quite gentle things really, and they respond to gentle handling.
You can actually end up with a really close bond with a hamster. Our last one was absolutely my baby and would sit and go to sleep on my knee.
Main thing to remember is - their behaviour inside their cage (their territory) is very different to their behaviour outside the cage. Inside the cage they are thinking an invader may steal their food.
If you do need to do anything in the cage - spot cleaning is best at first rather than big clean outs - then maybe do it when she's asleep and quietly (ie tip any food out of the wheel quietly! She is more likely to hide from you than run at your hand. Sometimes they follow your hand around just to check what you're up to.
They scent mark their cage and everything in it, partly to help find their way round (they don't see well at all, so scent is everything and your scent will become more and more familiar) and also to claim it as theirs. It's best to leave the nest and hoard alone unless it's pee'd in.
Keep coming on here with any questions. There are tried and tested ways of resolving any issues - and especially when it comes to cleaning time, because there are ways of doing it to avoid stressing the hamster.
Our current Syrian Newt doesn't like to sit still long
And a couple of our last Syrian who liked cuddles. And our bathtub taming.