I have a mature 8 yr old. She is very strong willed and likes things her way. She does what children do and pushes the boundaries a lot.
If I acted with her the way you seem to be acting with your dd, I think we would probably fight a lot more.
We negotiate, discuss and deal with issues. If she doesn't do what she is asked, I ask her if she wants to do x activity. If she says yes, then I tell her she needs to comply with y. I do this in a calm way and without putting her on the spot and if she gets stroppy about doing as I ask, I give her maybe 15 mins to process and don't expect her to immediately do something NOW.
Your punishments are confusing, the boundaries aren't clear. You are expecting way too much of your dd. If my dd back chats me, I give her "the look", say "oh dear, do you want to do x activity?" If yes, then she'd better change her attitude. That's usually enough. If not, I then warn her one more time and if nothing changes, take away the activity. She knows I follow through. And yes, the last time I took away an activity, I gave her the opportunity to earn it back and she behaved extremely well for a couple of days and her behaviour has been much better since. She knew how lucky she was.
Like a pp poster said, the rules and boundaries are clear. I don't have many of them. But my dd knows what is expected of her. If she isn't allowed something, it is confiscated. She may be mature but in many ways, she's still a little girl. I'm sure you love your dd to bits. It really would be great if you could take some time to see life from her point of view.
People I know at your dds age let their child go on his 2ds for 15 mins a day and he could earn extra time for good behaviour or helping out. I thought that was a great idea. And again a very clear boundary with positive results. Dd isn't into screens so not something I need to do.