Which makes it the Closed Sicilian.

No it doesn't. White could still play an Open Sicilian with 3. d4

Aiming for a Closed Sicilian, seems like.

Shows how much more I have to learn, as I thought that we already entered the Closed Sicilian with black's previous move.

4.e5 looks feasible, here

Yes it is! After 4.....Ng4 5. b4! or 5. e6?!

I would've just played 4.e5 right away.

This exchange is probably better than the tempting looking 5.e5!? Nd2 6.Nxd5 Ndxe5 7.Nxe5 Nxe5 8.d4 Qxd5 9.dxe5 Qxe5 and now 10.Bf4! Qxf4?? 11.Bb5ch mates. But if Black leaves the proffered bishop alone (11...Qf5), the game looks even.

gameknot.com

This is another game that I'm gonna have to look up. In fact, there are now many different openings that I'm gonna start studying. Doesn't mean that I'll play them with how little experience, but this would be done so that I know the main lines.

No harm in looking around to find out about w3hat openings there are kicking around. But for you own repertoire, I'd suggest at this stage to stck with a few you feel comfortable with. Say, start with e4 for White and look at Giuoco Piano, Closed Sicilian and Advance Variations in the French and Caro Cann Defences; and for Black, work out a reply to 1.e4, to 1.d4 and to 1.Nf3/1.c4 types of openings. Become familiar and comfortable with them, with several games under your belt, then you can start branching out. My own opening repertoire has always been fairly narrow.

Which had to have 7.Ne4, at the very least, just as good.

Which is what I think that you just did.

(!) Seems best. Keep the c-pawns doubled.

That's also my way of thinking here.

I almost certainly would have played 10.Nxc6 here.

I wouldn't have, but it's only because I would not be comfortable with exchanging, as white. I guess that it does favor him, though.

Presenting White with the opportunity once more to isolate Black's Q-side pawns. Instead, 10...Qc7 looks to be the go.

Fritz's first thought is 10...0-0 but it soon changes to 10....Qc7 - but then changes back to 0-0 - so they are both good moves!