This is difficult. Personally I would cut down the house rules to an absolute bare essential minimum - e.g eating a meal on the couch isn't exactly worth falling out over - maybe you need to relax that rule. She is doing it because she knows it will pull your chain - if the chain is taken away she has nothing to pull.
She is fighting for control, so ..... give her some! Ask her what things about home life make her irritated, and ask yourself if some of these things really are essential. Negotiate. If she hears that you are listening to her and her thoughts are valued, this could go a long way to establishing that you do understand she is growing up and needing a greater say in how she runs her life.
But there also need to be some "bottom line" rules that are non-negotiable. They will be different for each family.
Examine the things that you fall out over and see what the triggers are and how it might be possible to change things a bit.
The more she sees you as trying to control her opinions, thoughts and actions, the more she will fight against you and make your lives miserable.
I had some very strict ground rules: no-one is unkind to another family member, no-one shouts or swears at anyone. But outside of these I was pretty flexible with my DDs when they were teens. If they fancied eating on the sofa in front of the TV, then fine - sometimes I fancy doing that! - although I might say "It would be great to have you at the table; I would love to hear what you have been doing." But outside of that I gave them choice as far as possible.
It is about adapting to the idea that this is a young adult in the making, and asking what your rules for another adult might be - clearly that is not the total picture, but asking that sometimes allows for a bit of leeway.
Being a bit more flexible does not weaken your position with her; rather it strengthens the relationship because you are listening to her and she will value that.
Homework - well, I used to say to them that I fully understood this could be burdensome - and that some of is is pretty crap in terms of educational value - but that I was aware they knew why they were doing it for their own future, and that I trusted them to do what was needed..... that they were not doing it for me, but for themselves. Taking it out of a context of creating yet another opportunity for conflict can be a valuable move.
And as the teenage years progressed I used to say: "Get pregnant if you must, but never get in a car with someone who is high on drugs or alcohol!" They knew there was an element of tongue in cheek about it and smiled, but they also knew it was an expression of love and had a very important underlying message.
Maybe you need to renegotiate the rules in light of your DD's changing into a young adult. I am sure she does not really want to be at loggerheads with you all the time, so give her the chance not to be by respecting that she is getting older now and having more choices is a reasonable move.
Rules are important so she has boundaries and knows right from wrong; but rules that are not essential just present opportunities for conflict.
I had a friend whose OH was yelling at his teenage son to take his beanie off in the house - why, just why, does that really matter? It is just a focus of conflict which he was handing to his son on a plate. It was a platform for the son to assert his independence. Take that away and you take away the conflict.
Pick your battles! Hand back come choice! And tell them you trust them to make thoughtful decisions - so that with more choice comes more personal responsibility. Blind obedience is not appropriate at this age.