Was my strategy correct? (Moves 13-22 appx.)

This is a game I won, but only because my opponent made two elementary blunders - he made a horrific positional move that blocked off both of his bishops and made them useless, then hung the exchange. 

However, during the game I was unsure of how I should play (as often happens in the closed sicilian), especially how I should activate my pieces during the early middlegame stage. 

Here is the game, and what I was thinking. My strategy during the early middlegame was essentially to activate all my pieces, and then maneuver around (kind of aimlessly) until black made a misstep. There was nothing direct I could do, I felt, and my general strategy when this happens is to make moves that seem logical, keep my pieces active/ready, but do not "attack" anything. 

I was thinking about it. c4 is a very typical move white plays in this structure if the black pawn is on d5 instead of d4. Here, I was worried about having to defend my weak pawn on d3. 

Spent a while looking at the position before move 13. Haven't used an analysis board or engine or anything. Also, as a disclaimer, I usually underestimate pressure against the king. There are just my general thoughts:

I evaluate the minor pieces as about equal. Be7 and Nf3 could use some improvement. Bc1 and Bc8 definitely can. Black's king is definitely less protected, but I don't see a way to get a lot of pieces over there quickly. e6, f6, and f4 block paths. Maybe in the future f5 could start some kingside action.

But what I mostly see is all the weak pawns. a7, c6, c5, and e6 all look like nice targets. Ideally I want to put a bishop on a3 and move the f3 knight to c4. Sure that does bad things like hang f4 in the short term, but that's the sort of idea I'd aim for. Add in Rc1 and c3 successfully and you'll probably win 3 pawns (c5, c6, and d4). Maybe I'd start with b3 with Ba3 in mind. Anyway, kingside play isn't on my radar for white.

You're correct that black has a ton of weaknesses, which I thought about.

The reason I decided to play on the kingside was because I didn't see, tactically, how I could go say, Nf3-d2-c4 (keeping the other N on e4) without issues involving Ne3, which threatens Nxc2/Nc2. I would have to move my rooks to prepare for that, to avoid the fork, and I still wasn't sure if it would work or not. The computer says that Qh4 is inaccurate, and I believe it's correct, since black can shrug off kingside attacks if he plays correctly (didn't happen). 

Right now, my biggest issue in chess I would say is finding tactical justifications for my ideas. I just couldn't calculate if the maneuver was feasible or not, or if black always has some chance to get a tactical shot in.

If the structure was a bit different, with the black d4 pawn on d5 instead, and say the black knight on Nd7 and the white knight on a4, I would 100% go b3, Ba3, and get a totally winning position. I first saw this idea in the Grand Prix playing against a 1900 player OTB, and I'm proud to say I found this idea myself over the board, and was amazed at how quickly black's position got demolished - pawn down, white's complete domination of dark squares, and black's useless light squared bishop. 

Both of the above suggestions are better than Qh4, I've found. On move 13, instead of Qh4, c4 was declared the best move by stockfish, although there was a pretty significant tactical justification.

Although the engine didn't consider the Nfd2 idea, I fed it 13.Rf2, and it actually thought it was a decent idea - for instance 13...Kh8 14.Nfd2 Ne3 15.Nb3 and white is much better, because Rf2 guards c2. Kingside play was the wrong idea. It's just that it's the grand prix attack, and so I'm biased towards it (and in general, I would say).

I'm really happy  Because I'll probably get structures very similar to the one here in future games, and now I'll know exactly how to play. 

The kingside stuff doesn't seem so bad after I see it. It's definitely something I tend to underestimate. An idea that I didn't consider at all is my engine's suggestion of 17.g4-g5 trying to break up that pawn duo and open lines. I tend to be afraid of moving pawns in front my king, but after I see it, I like it. You did a similar idea in the game (although like you said, black's 22...e5 is like positional suicide).

Haha when you play the Grand Prix / Closed Sicilian lines as your main opening against the Sicilian, you start to love pushing the pawns in front of your king. Sometimes too much. 

I lost a game against an expert once where I played g4-g5 in front of my castled king to win his Bf6 for 2 pawns, because I was so desensitized to king safety, and I thought I was much better, but actually he started an attack and won.

The Grand Prix becomes difficult to play at the higher levels when black has effective setups to counter it.

But I've played it throughout the lower intermediate levels, with great results (I'm surprisingly undefeated in that opening, and I've had the chance to use it in 3 prize-determining games, of which I won 2 - against a 1500 and an 1800, and I drew 1 against a 1900... these were when I was playing in lower sections, of course). At the lower levels, they don't know how to neutralize it OTB.

Here's the game I played against the 1800 at a World Open, which secured me a shot at a top prize. I still remember the important parts of that game: