If you're still playing the game in question, I don't think we can help you yet. You'll have to wait until the game is over.
After 1. e4 g5!?
My fault -- I should have explained that this was a skittle. Eventually I lost a very interesting game. When I did a post-mortem I decided that with best play I wouldn't have been able to hold the g5 pawn, but I don't know how accurate my analysis was.

Stuff like that is debated among superGM's... some believe that taking the positional edge that comes with making the black bishop 'bite on granite' is worth more than the pawn. How much is counterplay worth to you?
PS: I take the pawn simply because I can't stand to see a move like that go unpunished to its fullest extent... likely the sign of a massive ego :P.
I continued 2. d4 Bg7!? 3. Bxg5. Then my opponent played 3...c5 and I began to wonder whether my grabbing the pawn was such a good idea.
Maybe shoring up the center with 3. c3 would have been better. Any opinions?
I often play this with black in rapid and blitz games. It is called the borg defense (the grob attack (1.g4 d5) played by black instead of white in response to 1. e4, (borg is grob reversed)). If white doesn't know how to proceed he's in big trouble, especially in blitz and rapid games when time is an issue. Best continuation for white is 4. c3 cxd4 5. cxd4 Nf6 6. Nf3 Qb6 7. Qd2 Nxd4 8. Nxd4 Qxd4 ( 8. Be3 is bad for white because of 8. .. Nxf3+ , another option for black is 8. .. Bxd4) 9. Qxd4 Bxd4 10. Nc3...
This leaves black with no option but 10. .. Bxc3 as 11. Nd5 or 11. Nb5 would pose an undefendable threat to square c7. Now black is hopelessly underdeveloped and both his King- and Queensside are left weak. 1-0
1. e4 g5
2. d4 Bg7
3. Bxg5 c5
After 4. c3, Black can reply with Qb6, increasing pressure on d4 and attacking b2. How can White defend this?
i would likely do this. i play the same way as black against the grob, giving up the rook on a8. it looks better for white whether he takes on c5 or plays d5. i don't see a way for black here to improve on white's side of the grob, but maybe someone can.

1. e4 g5
2. d4 Bg7
3. Bxg5 c5
After 4. c3, Black can reply with Qb6, increasing pressure on d4 and attacking b2. How can White defend this?
Stockfish suggests 5. Nf3, so a Poisoned Pawn variation:

Here's a stockfish continuation of your 4.c3 -- it looks scary as heck at first for white, but ends with a decided advantage if he can hold on
(total tangent: can anybody explain the 11...Kf8 move?
I continued 2. d4 Bg7!? 3. Bxg5. Then my opponent played 3...c5 and I began to wonder whether my grabbing the pawn was such a good idea.
Maybe shoring up the center with 3. c3 would have been better. Any opinions?