It's called Queens pawn game.. Its often employed by players who are not confident with the Queens gambit so play e3 to prepare a safe c4 push. I think its better to learn the Queens Qambit or just not play 1.d4. Another position it can lead to is where white plays c3 and Nd2 and Be3 with the idea of an eventual e4 push.
4.h3 This move is very passive and can hardly be even be called prophylaxis because blacks B can't move to g4 to pin the Knight.
4...c5 Yeah nice aggressive response contesting the centre.
5. dxc5? giving up his central pawn for your secondary central pawn with a loss of tempo.
*...Ba6 I would have retreated the strong dark squared Bishop to d6 here leaving his Knight pretty much useless on the edge of the board. Your way worked out strong too but if he had played Bxa6 before Nxc5 then he could have castled after and only been somewhat worse imo.
You played it exactly the same way I would have up until ...Ba6 so imo opinion you played it right.
I won't comment on the rest of it but it looks like a nicely executed positional squeeze to me. good combination to finish it. Nice game.
1 - Do any of you guys know this opening? Did I reply correctly?
2 - Some times its good to lose your queen (or two turns at least)
3 - This is the worst possible time to resign