Help me analyze 2 games?

I just played two games in live chess against the same opponent, lost one and won the other. Any help analyzing would be much appreciated. I've annotated the games a bit for your convenience.

In the first game:

6...Be7

9...Bc8??, your knight is attacked twice and defended twice. You could have simply castled. If you were worried about him removing a defender with Bxf6, that fails because Nxf6 and your knight moves away from the attack. 

Second Game:

6. h3, although not forced it wasn't a blunder. 

8. c4 is a great move if 8...cxd5 is a forced response. However black can put your center to question and introduce complications with 8...f5.

11. Ng5+ and Nxe5+ are pretty equal. Kg6 is not a good alternative for black since 12. g4 Bxg4 13. Qxg4 fxg5 14. h4! h5 (trying to put the queen to test) 15. Qe6+ Nf6 (if Kh7 then hxg5) 16. hxg5 and you gain much more material. If black tries 12...fxg5 then 13. gxh5+ Kf7 (other options lead to mate, Kf6?? Qf3 and Kh6 Bxg6 Kxg6 Rh1 Kf6 and you have the same position pretty much after the Kf6 variation. 

18. Bd7??; as you noted just drops a piece. 

21...Rxc5!; if 22. e6 then Ne5, if 22. exd6 then Nc8. In either case your passed pawns are stopped. 

Thanks for the help. I did consider 6... Be7 in the first game but if he just moves his bishop back then my knight seems to have nowhere to go, unless I move it out to the side and castle long (since it'll ruin my pawns if bishop takes)

And ya, my last move was obviously pretty dumb, that's why I resigned, I did consider castling and followed similar reasoning as yours but for some reason I dismissed it. That actually tends to happen to me once in a while: I will find a good move, but dismiss it without following it through completely.

I do agree that you will still have trouble with your knight, I just thought that it looked better since white can target your backwards e-pawn and you don't have too many options to defend it (since your bishop is at b7).

In the second game, what about 39...Ra4 stopping Rh4?

Interesting, I didn't even consider that!

In the second game black has an easy win if he plays Ra1+ rather than Nxh3. You can see how in this analysis:

I am no expert on this opening but 4...d5 in Game 1 does not look right to me. Your idea of b6 and Bb7 is fine but why play ...d5--Your King side development looks hard to complete

After 5 e5 it kind reminds me of a bad French for Black--how are you planing on developing your K-side?

I also do not like 6...f6 further weakening the K's position especially along the h5-e8 diagonal.