To answer your first question, there is still play left and even though you are down a pawn, the rating class you are playing in REQUIRES that you NEVER offer draws and play until the position is a theoretical draw. Your opponent can and will make mistakes quite often and you miss out a lot of learning experiences in chess if you offer draws in positions that still have life in them.
Fun things to do here in this position:
- Activate your king and slow white's progress on the Kingside...this will be where ALL of white's winning chances are ... so you might as well make it difficult for him.
- Given how much closer your knight is to the a3-b3 pawns, go after them either by trading/locking pawns and then using your knight to go after them via Nc3-Nb1 etc.
Not saying either of these will be a sure fire way to hold or even win the game, but playing on with "a" plan is way more instructive than offering a draw, even if you are down material. (unless there are stakes involved, for e.g. a tournament round etc.)
I haven't been playing chess for long, and I obviously still have a lot to improve upon. Here is a recent game of mine:
The game ended in a draw by agreement, because I didn't think that I would have won. Could I have won if I didn't offer the draw?
How else could I have improved my game?