Hello, Steven. A first try:
1. "Early" is the contrary of "late" (I arrived early at the station). "Soon" means in a very short time, and refers to a near future (We'll soon be at the station)
2. I'd say "you should excercise" ; then I'd choose "every day", but "each day" is also correct.
3.You don't use "were" because "damage" is in the singular.
4. It means that "we offered to ourselves the pleasure of going to a movie"
5. the second one is OK; you don't begin a question with a preposition. You can also say "Whose car is this?"
6. Both sound correct to me.