13.Rhe1, which encourages Black to castle, would not have been my choice. 13.Bxe5 would pin the Knight to the g7 pawn, and then if 13...O-O (to defend that pawn and anticipate 14.Rhe1) 14.Bxf6 gxf6 15.Rhe1 leaves Black's pawns split and open to attack.
Also 18.Ne4 is probably better than 18.Nd5, since it attacks the c5 pawn. In fact, it's hard to see how this can be defended. Play might continue 18..Ne5 19.Bxe6 Bxe6 20.Nxc5 Nxc4 21.Rde2 (the A-pawn is immune because after 21..Bxa2 22.b3 traps the Bishop and kicks the Knight)
Even simplier might just be 18.Bxe6 Bxe6 19.Bxc5. In fact, that is probably better than either Knight move.
This is probably the most in-depth analysis I have done of a game. My opponent hung a piece that cost him the game, but I thought the analysis up until that point could be useful to some players in my rating range. Any errors in my analysis or things I overlooked would be greatly appreciated!