Philidor's Defense

I probably would have played 3.d4 and taken more control of the center immediately, but there's nothing really wrong with Bc4. You are right to question 5.Bd5. It screws with his pawn structure more, but you just have to move him around more -- better to save the tempo and continue developing and overwhelm him. 6. c3, 6. O-O and 6.Nbd2/Nc3 keep more tension. Since you're already ahead in development, and his queenside pawn structure is amok, I like c3 to strengthen your center. 9. ...f5? is just a terrible move, almost losing outright, since your B on b3 now keeps him from castling and you have too many pieces active in the center. After that he didn't have any real options. Your opponent was pretty miserable (didn't see even the simplest threats) so it's hard to say more. I hope this helped.