Hello, and welcome!
I would love to help, but just need a little more information in order to assist you better:
How long do you have your kitten?
Is she spayed?
Is she an only cat/pet?
How do you react when she does these things?
Has she always exhibited this behavior, or is it new?
Thanks for all your additional attention and after you reply, please allow me some time to go over it and then compose and send your answer.
Her biting is her way of asking for attention. I'm sure she's not being deprived of attention, but when she wants it, she gets your attention by biting. She feels negative attention is okay, even if you tell her 'no' or however you react, because it IS attention. Many cats who were separated from their moms and/or siblings at an early age are not well socialized and were never really taught how to behave properly, all the time. Typically, in playing with their siblings or cat mom as babies, they are 'reprimanded' in 'cat actions' when they bite or are being annoying.
Sometimes, there are warning signals, before a cat will bite, like ears back, eyes dilated, tail slapping or swishing very quickly, and you are able to stop the 'attack' before she can bite. She's not doing this to hurt you; I'm sure you know that, but she's doing it because she considers you her 'littermate' and this is how cats play. If she wasn't socialized properly by her mom and siblings, she was never taught when enough is enough.
When she exhibits this unwanted behavior, leave the room after telling her firmly 'no bite' (don't yell, just say it firmly), and then return in a few minutes. If you're consistent with this, when she sees she's deprived of your company when she bites, she'll start putting two and two together. Another good way to keep her from biting, is to gently push her away with a pillow, when you either see the warning signs, or after she has already begun the attack. Speak to her gently, but firmly and say something like, 'no biting; you're hurting me!' Of course, never use your hands/fingers, feet, toes as playthings for her.
She should have many toys and a couple of scratchers and if she doesn't yet have one, she would enjoy a tall kitty condo or cat tree with different levels, shelves and 'hidey holes.'
Have a good play session with her, so she can get some good exercise and become tired out, before you start watching tv, by encouraging her to play on her kitty condo and/or with you throwing toys for her to chase and also playing with interactive toys, like a laser pointer and feather wand (fishing pole toy). Also, feed her a small meal at that time, so she will take a bath and hopefully, sleep, so she doesn't intrude on your relaxing/tv time at night.
Here is a great list of toys she will like, below, and if you separate them into groups, let her play with one set for a few days and then change to another one; she'll feel like she's getting completely new toys!
Feliway, a cat calming pheromone, will help. It comes in a plug in diffuser, so you can put some around the house. It also comes in a spray, but for your purposes, I think the diffuser would be best. Only cats can detect it; it has no scent to humans. Here is more information:
If you add these things I've suggested, to enrich her environment and keep her busy, you will hopefully see a decline in her biting.
As far as the jumping up on someone standing and digging in claws, this is also common behavior for a kitten, but again, gently tell her 'no' and remove her from that person. This has happened to me and I know it hurts. It's like she thinks you're a human scratching post!
I'm glad you started clicker training her and giving treats for good behavior; that was a very smart move on your part!
I hope all will be well!
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