Unfortunately this is the reality of life with a kitten. My 8 month old kitten will chew threw any garbage bags and distribute the rubbish around the house if I am not careful. A lot of people don't realize the work that comes with having a kitten, and her behavior isn't at all bad. It is normal and to be expected. We often forget these are wild animals at heart and they don't see our homes the way we do, but rather the same as an outdoor area where they can do what they please.
With my cats, this behavior didn't settle down until they were just over a year old. My older boy, who is 18 months old, is a perfect gentle man and while he loves a good game of chase and he still knocks stuff down from time to time, he is much more mellow.
This is where you are going wrong, I believe. With any animal, your goal should never be to control them. This is where you will hit a wall, as it is impossible to control a sentient being with individual thoughts and agenda. You need to coexist I have found more success in changing my habits rather than my cat's. You need to coexist. So basically anything of value is stored in my room or a cabinet, which is a no cat zone until my kitten matures and I keep the door closed. Nothing left on benches, dining table etc. The toilet door is kept closed to prevent him getting the toilet paper. The trash can lid is duck taped shut so he can't get the trash out if he knocks it over. Any sliding doors have jams in place so he can't open them.
Unfortunately with cats, there are very rarely any 'no cat areas'. Even if they learn not to go on these surfaces when you are around, you can bet they will get up there when you are gone. You have to condition yourself to understand that if something is destroyed, its not because the cat is being naughty, its because you didn't put it out of reach. Would you blame a baby for burning itself on a pan you left on the stove?
I think your kitten is very bored. Having toys often isn't enough. You need to be interacting with her, getting her to chase the toys, challenge her to burn some energy for at least two hours a day. It may even teach her to associate the toys as things to play with rather than your stuff. Even taking her for walks is great if you are able to do that.
I think this may be contributing to her hyperactivity, as she is unable to expend her energy for periods of time and therefore has too much when it is time to let her out. For about 4 hours a day would be ok while you aren't at home, I believe, but not overnight IMO. Perhaps just shut your door.
The fact that she doesn't like the treat is probably a main problem with your training progression. Why would she do what you want for a treat she doesn't want? Try finding a treat she LOVES, not just likes and see how that goes. I do believe clicker training a cat is quite difficult though. It sound to me as though the approach you are taking to her training is similar to one you would use for a dog. This likely won't work, as they have very different psychology form what I have observed.
Yes, there is a reason. Cats don't perceive things the way we do. She sees no difference between her cat scratchers, toys etc and your belongings. You could try some citrus juice, cats generally don't like those, or some scratch deterrent sprays from a pet shop. I have a sheet covering my couch to limit the damage from any accidental scratches.
You may want to try some raw chicken wing tips, these are great for dental health and boredom and will five her something to chew on.
Don't try to restrain her, and put her straight back down. Avoid contact completely and even leave the room. Biting and scratching equals no attention. Or even replace your hand with one of her toys, if you prefer.
With my cats, this behavior didn't settle down until they were just over a year old. My older boy, who is 18 months old, is a perfect gentle man and while he loves a good game of chase and he still knocks stuff down from time to time, he is much more mellow.
Never feel guilty about this, If you can't provide the life this kitten needs without destroying your own, then it is best for her to go back to the shelter and find a home better suited to her. Cats aren't for everyone, and if you can't coexist with each other then returning her may be a kindness for you both.