didn't look at all the games but I think 7.Nf1 in Game 3 was a positional mistake.it allows the immediate 7...d5 which forces exd5 and then your d3 pawn becomes a target.(which is what happened in the game). instead 7.0-0 is the better move...and here's how the game could go:
Should've sat on my hands!

In the first game After 24.Rxd6..c5 White could convert his advantage of the exchange into a Rook vs Bishop endgame.

Thank you CerebralAssassin and paulgottlieb for examining and sharing your insights on my third game. I'll keep in mind castling when an opponent has the possibility of breaking open the center. I'll also try to put more thought into my opening moves instead of jumping into a system by default, which is something I didn't realize I did.
Thanks, mateologist, for pointing out that tactical rook capture. I was thinking about a knight fork in that position, with the active knight and all, but didn't notice it during the game. Also, I greatly appreciate your advice on the endgame (and on simplifying to a winning endgame), since I particularly need work on those areas.

In game 1, why go after the rook instead of forcing the knight trade and making it an easy win?
I didn't realize that would be an easy win! What makes it easier, and what would be white's strategy in the ensuing endgame?
The reason for forcing the rook trade was because I had the impression that rook endgames tended to be drawish, so getting rooks off the table would avoid such things.
The following is a series of 15-minute live chess games, filled with brilliantly horrific blunders. I'll do my best to analyze each game (both objectively and subjectively) to learn from my mistakes.
Game 1:
Positionally speaking, I should have planned the arangement of my pieces better. For instance, an early castle would be an improvement, seeing that black's bishop was unavailable for a pin, after which I should have aimed for a faster queenside expansion, while black struggled with bishop placement.
Game 2:
In game 2, I had a clearer plan and execution, although I had a shameful blooper along the way. I barely used my 15 minutes, and should have sat on my hands while considering the best ways to improve my position, and more importantly, not drop pieces all the time.
Game 3:
This third game confused me a bit, positionally. At this present moment, I still fail to see the positional blunder which from which my loss stemmed. Obviously, white's d-file pressure was strong, but the error was somewhere in the defense. Perhaps move order was an issue here.
Game 4:
The third game has little to see, but illustrates that the loser is the last to err. Clueless but tactically accurate play is better than decent moves combined with the occasional horrific blunder.
Lesson learned? Gotta sit on 'em hands!