How to avoid these "giveaway" losses


I failed to count attackers and defenders on that one. For some reason I thought I had enough on the back rank to capture any attacker.
Game 1: It's the position after 16&17 that has flashing red lights for me. Q and R attacking e1 with the N at e5 being able to move out of the rook's way with a check. The endgame does not immediately look like an easy win if you have no endgame experience and no time on the clock to think.
Game 2: Practice mates in 1-2-3.
Also, you are really up in material but behind in development here. I'd (safely) trade as many pieces as I could in that position to simplify the game.
A few remarks:
1. In both of the games you play Bd3/Bd6 which makes it difficult to develop the other bishop. In the second game this allowed the fork, which led to an equal position instead of you being a piece up. (Your opponent misplayed the Ruy Lopez badly in the opening.)
2. In the first game there were a number of tactics that you missed, for instance 22. Ne7+ Kf8 23. Qxd6 Qxd6 24. Bxd6 would have given you an endgame a pawn up. The good thing is that you don't hang pieces often, but learning other tactical patterns will be useful.
3. The endgame of bishop+knight vs rook is rather equal but difficult to play for a beginner. Your queenside pawn moves were definitely not in the right order. Tentatively I would say that b3(prevent c4)-c3(strengthen hold on b4)-b4 would be a better order, I'm not sure if it's the best way to play it (see the lesson on pawn breaks). In addition, it would have been better to blockade the passed pawn (but this is tricky with the knight + bishop combination, the problem is that the rook can remove the blockade before your other piece can capture the pawn), not to capture it with a piece losing it. After losing the piece you had no chances with the worse pawn structure.
4. When you are up on material, trading pieces is a good idea. With less pieces on the board, there are less chances for counterplay (as long as there are no passed pawns).
5. In the first game there was a draw by repetition available (28. Ne7+), sometimes that is a good choice if the endgame is uncertain.
Many of my recent losses have been giveaways, the report telling me that the game slipped through my fingers. I feel that most of my losses are not "bad" losses, just that my opponent played that bit sharper.
I'll post below my two most recent giveaways for a second/human opinion and perhaps glean some insight into what I need to concentrate on going forwards.
In this game I was ahead from move 11 up to around move 33, after that it was Black all the way.
In this game I was also on the front foot despite a couple of blunders, until the final few moves when I fell to a back rank mate.
I feel these losses more than if I lose a game due to really poor play.