My advice would be "hands off" as much as possible- decide what is worth arguing over and leave the rest. I had a very stormy relationship with my DS- see post below" and realsied too late perhaps that you cannot make them do things.
I would leave the homework etc up to school, apart from maybe a weekly nag- I used to be a sec. school teacher- as long as they know you care, that's fine- but leave it up to them to put the pressure on- if need be, go and talk to them and devise a strategy where they will nag, not you.
Food- give him what you think he should eat- or he goes without.
Leaving a mess- say whatever is left on the floor or around the house will be thrown away- unless he clears it up by the end of each day.
It is all normal stuff to rebel, but kids need boundaries and they are testing you- my only advice is to realise that you cannot control everything, so decide what is most important to you.
Has he got a Dad who can step in and check him for the rudeness?
You could also bargain with him- rudeness=no lifts/pocket money/whatever.