Inadvertent gambit

I last played actively 50 years ago, when i was around 1800. Taking it up again, I find I'm very rusty. In this game, I think I had good positional ideas, but sometimes played impulsively without calculating tactics, sometimes missing obvious things. In this game, Stockfish has me ahead most of the time, despite some blunders on both sides. At the end, I resigned because I couldn't see a way out, but Stockfish has us even! I'd appreciate comments and advice. 

I had to look this up on 365chess. The move 6. Bc4 isn't even listed there. The usual move is 6. Nc3 with each side having a 38% likelihood of winning, and a 25% likelihood of a draw.

Another idea was 8. Nfd2, intending to follow with 9. f3 to attack the pinned knight with a pawn, though I don't see that White gets any edge after 8. Nfd2 Qe7 9. f3 Nxd2 10. Bxd2 Qxe2+ 11. Bxe2, and in fact White has just lost at least one tempo in that line.

You missed your big chance to get the pawn back with ease and to get even with the simple 9. Bxe4 fxe4 10. Qxe4+. Is this another case of overlooking a backward piece motion for capture?

No, I was just following a different game plan. According to Stockfish, I have more than enough compensation for the gambit pawn, and his f pawn is weak and can wait. I liked my B on d5, and planned to support it with NC3 as soon as I could chase the N of e4 away. Such at any rate was my line of thought.I could have prevented 9.d4 with 8 c3

I don't like 4.....c5 for the ideas you mentioned, ie; big hole on d5.

What happens on 6 e5 ?   if Black plays 6.....de  then 7 Qxd8, Kxd8  8 Nxe5 and White should have an edge.

Not so sure what happens on 6 e5, Qe7    Quick development with 7 Bb5+,  Bd7  8 Bxd7, Nxd7  9 O-O does not seem to work asd Black has Nxe5.   If White has a better 7th move, then the aggressive 6 e5 is good.

yes, 8 B-d5 is a superior move !   Well played sir !!   though unfortunately, looks like you would have to cash in by exchanging it for Black's advanced horse plus a pawn.