1. I was moved enough to want to help her. ( Is this grammatical?)
2. I was all wet after I washed only the first dog. (Does 'all' mean 'completely' here?)
3. Today was best.
4. Today was the best.
(Which one is grammatical?)
1 is fine, yes.
2 is fine, and yes "all" means "completely" here.
4 is best; I think I've heard 3 only in answer to a question.