From the shine of her abdomen i think it is safe to say she is in pre-molt, yes. Three weeks without food is no big deal for adult T's. Is she your first? Can you post pics of her and set up?
She is not moving as much because her 'old skin' is becoming too tight with her 'new skin' growing under it.
Arboreal T's also lose grip close to a molt because if the old footpads wearing out.
I'm assuming this is an A. aviculara from the photo.
A bald spot on the butt means that it has kicked all of the irritating setae off as a defensive action. That's nothing to worry about. Next molt, the hairs will be back.
A T not eating is something that new T keepers often freak out about, but 3 weeks for an adult is nothing to be concerned with. Some tarantulas will go months or even over a year between meals. All you need to do is keep the water dish filled up and wait it out. Keep offering food every couple of weeks, and take it out if it's uneaten. If it molts, hold off on feeding for 3 weeks so its fangs have time to harden.