It said I lost because when I turned away my opponent reconnected and I lost on time not knowing he had reconnected.
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Your opponent's 3...Qe5+ is not a very good move, it may seem to gain a tempo but actually loses one because the queen can get kicked around more. Your 4.Qe2 does not make the most of this advantage, because Black can trade queens and catch up on development. The best move is 4.Be2, which develops and keeps the black queen in the center where she can be harassed by 5.Nf3, gaining a tempo.
If you really wanted to trade though, 5.Qb5+ forces a queen trade by forking the enemy king and queen.
Your opponent's 6...Bxf3 is not best, the pin on the knight can be maintained by 6...Bh5, and because the knight is pinned the bishop is more mobile, and thus more powerful; also this loses the bishop pair for black.
7...f6 is, as you noticed, poor because it is unnecessary and allows 8.Qxb7
9...Nc6 was a blunder as well, allowing the crushing 10.Qxc6+ Kd8 11.Qxa8+ Kd7 12.Qxf8 winning two extra pieces on top of the rook you won in the game.
The idea behind 12.g4 is very good, restrict your opponent's pieces. 13.f4 and 14.Bc4, however, both simply lose material, which you saw after. Even if your opponent hadn't captured the bishop, Qa4 is not mate, your opponent can block the check with Nc6, which also frees up d8 as a flight square.
17...Nxg5 also simply drops a piece.
Overall, your most important things to work on are seeing the whole board, not just the part where you or your opponent are moving, and basic tactics. Books or just solving chess problems will improve your tactical skills and board vision, and playing more games to gain experience will help as well.
By the way, it was an interesting game!
You missed a big opportunity when you missed 10.Qxc6+, but I guess you were excited about taking his rook... after 10.Qxa8 you still had a winning game.
The move I would focus on as a bad move to learn from was 11.Qxa7?
You've got a raging attack going and you pause to pick flowers? Qxa7 very seriously diminishes your situation... You don't need to win a pawn, you have a commanding lead in material already. What you need is to continue your attack while his King is trapped in the center and put the game on ice! You need to unpin your bishop, castle your own king, develop your other pieces... you have important things to accomplish with your move 11... and Qxa7 accomplishes none of them.
The classic advice in a situation where you've got an early attack on the king trapped in the center (of the back rank) is: Sacrifice material to keep the attack going... 11.d4! ... if you're lucky he'd take the pawn and with that open e-file to work with (and your bishop unpinned) it's game over. Even if he doesn't take the pawn... he then needs to make a Queen move, which doesn't help him get his pieces out, and now you have another tempo to develop with... can bring out your dark square bishop... your attack is becoming unstoppable.
12.g4.... taking squares away from the N is a great idea in general, but it's not great right then. You want to get your pieces to good squares and get your King safe, and if possible attack his weak points. Instead you weaken your kingside making your king less safe, and since g4 doesn't attack him in any immediate way, he gains another move to mobilize his forces.
13.f4 is a really interesting move, tempting black to waste a move eating f4, which should allow you to gain tempo attacking his queen with d3, or even Rf1.... but you followed with the Bc4? blunder. Blunders are bad, but they happen... the thing here that needs to be corrected is your complete lack of urgency about bringing out your pieces. In this type of position you need to get your pieces into play, not just push pawns at him.
After this, you both blunder a bit (and more pawn pushing!) but i like the fork idea at the end. Too bad about the disconnect.
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Here is one of my recent games. It is not the longest or best example but it is one I wanted further analysis on. Any tips on how to improve would be appreciated.