Help me understand engine analysis on two positions.

In short if you're ahead in development and your opponents king is still in the center it is advantageous to open the center. There's no point playing f6 as the knight can't go to e5 or g5 anyway and you'll be looking to play f5 in the future.
15... Qb6 is a complete misunderstanding of the position. The b2 pawn is easily defended but that's not the point. You don't want that pawn anyway as you shouldn't open up a file in front of your king. In opposite side castling you play against the opponents castled side. So Rh5 Ng5 to exchange the defender knight without tripling your pawns or the more natural g5 immediately. You have an open h file, doubled g pawns, a knight in the center and white castled short, should be a clear signal where you should play.
@1
11...f6 weakens g6 and e6, e.g. after 12 Bd3. It does not develop any piece either. Better seems 11...O-O-O to castle your king to safety and to connect your rooks to activate them.
11...e5 12 Bb5 exd4 13 exd4 a6 is possible too.
15...Qb6 16 Qc2 gets you into more trouble. 15...Qd7 is more cautious.
However, the real fault was 13...dxc4? giving up the center, opening the c-file, and developing his Bc4.
In short if you're ahead in development and your opponents king is still in the center it is advantageous to open the center. There's no point playing f6 as the knight can't go to e5 or g5 anyway and you'll be looking to play f5 in the future.
15... Qb6 is a complete misunderstanding of the position. The b2 pawn is easily defended but that's not the point. You don't want that pawn anyway as you shouldn't open up a file in front of your king. In opposite side castling you play against the opponents castled side. So Rh5 Ng5 to exchange the defender knight without tripling your pawns or the more natural g5 immediately. You have an open h file, doubled g pawns, a knight in the center and white castled short, should be a clear signal where you should play.
This is fantastic feedback, thank you for taking the time to respond. I currently don't have any idea when it's advantageous to open the centre or keep it closed, so I'll look into that and learn.
Re: 15... Qb6 - again, thanks for explaining this - I never would have seen the position this way, and it never occurred to me the point of bringing out the rook is to exchange knights. Clearly I need to get better at reading the board. Just understanding that my weaknesses is this game are positional rather than tactical is a huge, huge help, so thank you!
@1
11...f6 weakens g6 and e6, e.g. after 12 Bd3. It does not develop any piece either. Better seems 11...O-O-O to castle your king to safety and to connect your rooks to activate them.
11...e5 12 Bb5 exd4 13 exd4 a6 is possible too.
15...Qb6 16 Qc2 gets you into more trouble. 15...Qd7 is more cautious.
However, the real fault was 13...dxc4? giving up the center, opening the c-file, and developing his Bc4.
Thank you for the response! So 13 ...dxc4, I wasn't thrilled about taking the pawn either, but my concern was that if I didn't take the pawn, he would march it up to c5 and i would waste time getting my queen out of trouble, and probably weaken my position. I think I was just outplayed at this point in the game, and was trying to find the least damaging move. Per the previous commenter's points, I think if I develop my positional understanding of the game I can improve. Thanks again for the comment!