Fighting is a common problem when you have children who are so close in age, and of opposite genders. (Ask me how I know. -_-)
What my mother did with my younger brother and I was to send us to opposite ends of the house and keep the house silent. I would be in our room, while my brother would be with her in the kitchen or the living room. The point was to not give us attention when we behaved badly. If we ever yelled at our mother, we were spanked. Never hard enough to leave a mark, but enough so that we thought twice before disrespecting our parents.
As for the trouble with meal time, if we didn't eat what was cooked for us, we simply didn't eat. There were child proof locks on the cupboards that were within our reach, and all we could have if we pushed away our mother's cooking was a piece of plain bread.
I've been told these methods seem draconian, but they work. My brother and I didn't grow up to be maladjusted or anything like that, but keep in mind that every child is going to be different.
I hope this helps you!