neither...I can hardly play chess let alone classify myself into a certain style of play
Do you consider yourself a tactical or a positional player?

Tactical. Definitely tactical. I'm rather decent at positional play, but tactics are my home ground. (That's why I NEVER play 1.d4)


Sometimes there is NO best move. There is simply a number of plausibilities all with roughly equal merit. What do you do then?

I'm both. I make moves that are tactically bad and give me bad positions.
yes this is my approach too although I have noticed a tendency of late to actually try to evaluate the resultant positions
Hmmm...OP's blitz rating is ~300 points higher than his rapid rating. With a 1500 rating, you're not classified as any type of player yet. None of us have a "style" until we're rated about ~2000+. Titled players laugh at players rated below that classifying themselves as either positional or tactical.
OP has a lot of work to do.
Actually from what I've heard it's the opposite Intermediate level players tend to be more specialized than Masters because Masters can't afford to be only good at one thing.

In that third game, 23. Bxf6 is slightly suboptimal.
Try 23. Rf2. This quiet moves comes with tempo... now fxe5 wins the whole rook, since black cannot unpin his rook with tempo (Rxf1+). He has only one defence as far as I can see, that's e3, driving the rook back to f1, but this pawn is no longer protected by the bishop and is an easy capture very shortly, and also it can no longer break open the centre with exd3. This quiet 23. Rf2 wins an extra pawn and results in a better pawn structure for white. I'm actually quite pleased to find that move, it's subtle. 23. Bxf6 is obviously winning too, but I like to play the best move.
Last few games of mine. I usually play quiet 1.d4 openings but decided to experiment with 1.e4 with good results.