For suspected engine use: use the report button, not the forum.
To answer the question: no and no.
Both players made a lot of mistakes.
Both players played too fast.
If you play badly, then admit that and take responsibility for your own bad moves instead of blaming divine intervention.
Neither cheated, don't accuse unless you are 99.9% sure. Make sure you check their centa pawn loss beforehand as well.
If your opponent plays the Philidor (don't play the Philidor, by the way), then you should play 3.d4 while you still can, as this already gives white a small advantage. If you play 3.Bc4, you will simply transition into a Giuoco Piano, which is equal. 6.Bg5 doesn't really achieve anything, as it does not pin the knight. Better was 6.O-O. 7.a3 wastes a move. 7.O-O was better. There was no need for 8.b4. Better, again, was O-O. 11.Nd5 loses a piece to 11...Nxd5. If 12. Bxd5, then 12...Bxg5. If 12. Bxe7, then 12...Nxe7. Better was 11.Ne2. 15.g3 was a bad move because 15...g5 wins your bishop, and because you have weakened your light squares without having a light squared bishop nearby to cover them. Better was 15.Bg3. 17.f3 was also not great, but your position is pretty hopeless anyway. 17. Qf3 might have been a more stubborn defense. I have nothing to say about the rest of the game.
Lessons? Seize the center when possible, develop your pieces to useful squares, castle early, and think carefully before moving pawns, because you can't move them back.
3. e3 is too passive, IMO. Better, probably, was 3. c4 or 3. Bf4. 8.a3 is a waste of a move. Seize the center with 8.e4. 10.g3 is bad for the same reasons as the previous game. 10.h3 was better, as it kicks the knight from g4. 13.Nxg5?? is completely ridiculous, but the position is pretty bad anyways. Better, probably, was 13.hxg5 fxg5 14.Bxg5 Be7 15.Bxe7 Qxe7 16.Kg2.
19. Qa4+, although a nice trick, doesn't work as shown in the game. 19.Kg2 was better (I think.)
I don't really have anything to say on the rest of the game.
I didn't use an engine to analyze the games, so there may be things I missed and parts of my analysis may be wrong. But I hope I was at least a little helpful.