1. I will go to a baseball game.

2. I like going to a baseball game.
2-2. I like going to baseball games.
2-3. I like going to the baseball game.
3. I like watching baseball games.
4. I will go to the baseball stadium to play baseball against the Tigers.
5. I will play baseball games against the Tigers.

(Are they all grammatical? What about #2, #2-2, #2-3? Are they all the same?)

All are fine.

2, 2-2, and 2-3 mean approximately the same thing, yes.