I too have a super strong willed child, my dd is now 3.5. Now, before I start, I am no expert and I always get told in this forum my ideas are bad, but I am choosing to post because I know exactly how you feel. It is really really difficult to parent a child that seems to have a stronger will than you do, and it is awful when other people suggest that you can beat your child into submission and that would be a good thing.
The tactic I have used when dd bit or hit me, was to tell her, I don't want to play with you when you do that, and I get up and leave the room. I go do something else. Usually dd comes to look for me and wants me to play with her, though sometimes she plays alone a while first. When she wants to play again, I generally do return to playing with her, though sometimes I discuss appropriate behavior first- depending on how much time has passed and such. This technique did not work the first 2 times, it had to be repeated Every time she was voilent, because she wanted to test me. And I have had to at times tell her "No, I don't want to play with you right now, you hurt me", because that is how I really felt. After implementing this consistently, my dd's behavior did get better about the hitting and biting.
On the subject of other behaviors, sometimes you have to rethink your expectations. For example- I make a point of serving my child a well balanced diet that I think should be appealing to a child, but I have made a choice that it is not my responsibility to make her chew the food. Actually ingesting the food is her responsibility, I just make sure its there. She'll eat.
I'm not sure I understand the computer issue. If your dc is trying to "use" the computer when you do, it maybe an attempt to get your attention and be involved in something you are engaged in. Unless you have to work from home, I might suggest limiting your computer time to times when your dc is otherwise occupied, so as to avoid the fight. Sometimes when children are doing these behaviors that make us nuts, its really about getting our attention. I have found with my dd that stopping myself and giving her my full attention like sitting with her to read a book or use blocks really helps. And sometimes I take her on my lap and let her push the keys.
I hope something in here helps. Being a Mom is really hard work.