How to play this opening properly as black?

So I encountered an opening sequence that I've never really seen before, surprisingly. I've seen it in a different Sicilian, but not in the 2...e6 variation before.

I made some probably bad moves that seemed normal, but I was behind in development and I'm not sure what the right approach would be, as black. 

How should one properly play for black? I wanted to play the Kan, and I think 3...d5 opened up the position too quickly, and ....Bd7 just hung a pawn. 

Where were my mistake(s)?

If you want to play a Kan , you have to wait White to open the center and not play d5. I think 3...a6 is your move , protecting b5 square and preparing Qc7 in case of d4-cxd4-Nxd4 but if White doesn't follow 3...a6 with 4.d4 forget the Kan and play Nc6. In principle you open with d5 only when you are ready to castle otherwise you might get in trouble.

Yeah, I just noticed that. 

What do you think about 3...Nf6 ? 

I think I'll stick to 3...a6 from now on. 

It's worth asking why 2.Bc4?! is a poor move against the Sicilian.  It's because Black can play an early e6, d5 and gain a tempo against the Bishop.  After the Bishop moves, likely to b5, you reach a similar position to the game.  In the game, though, White now has the extra tempo, as Bb5 comes in one move.

The mistake is playing d5 and opening the centre when White is clearly the first to castle.  White will bring a Rook to the e-file very quickly, and if Black tries Be7 then Qe2 and the pressure is real.  Be6 can be met by Ng5 (after a Nf6).  Black is not losing, of course, but he is under more pressure than necessary.

Said another way, in the first two moves, White has developed two pieces whereas Black has only moved pawns ... and also opened the position.  Of course White should be better.

3...Nf6 is vanualble to 4.e5 when Black has to choose between Ng4-h3-Nh6 or Nd5-Nxd5-exd5 were in both its not the end of the world, but I don't find them attractive either.

After 2.Bc4 Black is not obligated to play immediately e6-d5 but to prepare it. Black can play a6 first or Nc6-Ne7 fianchettoing the Bishop. In any case 2.Bc4 considered inferior to other Whites options because White has to spend tempo retreating the Bishop allowing Black to expand further he's center.

I have no problems against an early Bc4.

Also, 6...Nc6 seems to be better than 6...Bd7, in the above line I gave. More flexible, since the knight wants to go to c6 anyways. 

Objectively look at the position after 5. Bb5+ Nc6

White's developed 3 pieces to 1 that's pinned and is ready to castle. Black no King side developement. Black may as well dig a hole and and jump in. 

Amazing how 3... d5 which often works can go so wrong. 3. a6 had to played against 3. Nc3

I love playing vs Sicilian! Morra Gambit rules !

This is what I usually play. Easy to learn

You should play 11. ... Qh3! If he doesn't see he can take your queen you can laugh at him and say ha ha ha you could have had my queen, but if he takes it, you can try to win down a queen trying to take advantage of his poor pawn structure and laugh at him if he loses and tell him he better find a better hobby because he lost after being up a whole queen what worth does he have, and if you find that you are losing at the end, say it was a mouse slip, and ask him to resign.  If he doesn't accept tell him he has bad sportsmanship and that you are disgusted at his behavior but none the less are willing to meet him halfway and let him accept a draw offer.  If he refuses just say one word, REPORTED, and tell everyone on the forums how someone resorted to those type of refusals to be a good sportsman!

Are you the one who told us (about a day ago):

Really? If you wanted to play a Kan then play a6!