Once you get to know your hamster's personality then you will be able to find the answers to your questions. I don't know your hamster so can't really answer your questions but will try and give a general response.
1) that depends and is not necessarily a safe thing to do because a hamster can fall or jump off a bed. I'd put her in a playpen or a hamster safe area on the floor if you have one.
2) the water i give my hamsters is room temperature and don't think that it has to be cold. In fact, its recommended to give fresh food at room temperature and not straight from the fridge.
3) that's unusual for a young hamster not to run on the wheel. I'd check the wheel to make sure that it is working ok. Is it big enough? She may be running when you're asleep so put some substrate on top to see if its gone in the morning.
Try a whimzee dog chew. Most hamsters love those.
4) i don't know but some hamsters are like that, they sit still and sniff to check if all is well around them.
5) no idea because some hamsters are silent and others are vocal. Observe her and see what she's doing and what you are doing when she's squeaking.
Is she stressed or calm? I had a foster dwarf who would squeak loudly when woken by mistake.
6) uses it what for, to run through it or chew it? You could make some toys from cardboard tubes and hide treats like seeds in them.
7) sounds like perfectly normal hamster behaviour and make zure that she has plenty of substrate.
they do that a lot and wash their faces
You're a lucky hamster momma to have a hamster that is so tame already.