No. Black should be winning after he completes development.
Sicilian Defense: Alternatives
Gambits often give a pawn for positional play and or a lead in development.
2. e5? is a mistake and while Black's pawns are doubled, they dominate the centre

Well, no strong player in the last 100 years has chosen to play 2.e5 against the Sicilian. Perhaps they had their reasons. What were you hoping to accomplish with that move?
6...Bd7 seems like a good and simple move for Black. White has very little for the pawn.
In the final position White has pretty decent compensation, based on Black's horrible pawns, But 6...Bd7 would have prevented that.
Don't play 2.e5 again!
Well, it was a blitz game ; )
Had it been a long game, I would've played something more reliable like
I understand miellago98, but why play something that gives you a disadvantage?
It isn't even a trap! You are hoping that your opponent gets confused.
It is like playing with a pawn handicap!

Is there any compensation for White's pawn?
(This is from one of my recent games, which I actually lost in an endgame. Yet I still wanted to know if I played the opening correctly.)
You gave up a pawn for nothing. So to answer your question, no you did not play the opening correctly.

Sicilian Defense: Alternatives
Actually if you like the idea of playing b3.
It is an alternative line in the Sicilian Defense. It will make the game be different than some of the mainlines.
However, They play it at move 2 usually.
It is named the Snyder variation.
Sicilian Defense/Snyder Variation
ECO B20 1.e4 c5 2.b3
Yeah I do not think they give up any pawns for free though. It might be worth looking at.

I understand miellago98, but why play something that gives you a disadvantage?
It isn't even a trap! You are hoping that your opponent gets confused.
It is like playing with a pawn handicap!
Well, in that position Black has double isolated pawns, it won't be very easy to play with them.

Well, in that position Black has double isolated pawns, it won't be very easy to play with them.
I do not believe the position you are showing is that great for white.
However, I am more than willing to hear your idea's/agruement.
I believe the continution black played was a little premature.
What if black plays differently.
What would you do against this move. Considering I am still defending the pawn with my queen. I have not played f6 yet so I do not have any structure change either. I remain flexible.

Well, in that position Black has double isolated pawns, it won't be very easy to play with them.
I do not believe the position you are showing is that great for white.
However, I am more than willing to hear your idea's/agruement.
I believe the continution black played was a little premature.
What if black plays differently.
What would you do against this move. Considering I am still defending the pawn with my queen. I have not played f6 yet so I do not have any structure change either. I remain flexible.

Yeah I think I like the move f6 now. Now that your bishop has moved.
I will just castle. Now try to do something with your dark-squared bishop :P

I will just castle. Now try to do something with your dark-squared bishop :P
I am up 1 pawn. I do not need to move my dark bishop right now. He is doing great.
Your only open file is E file and my pawns are fortress there.
My open file is D file.
I will queen side castle and my rook will go there once I castle.
Than I will throw my G pawn and H pawn at you in a savage attack.
Is there any compensation for White's pawn?
(This is from one of my recent games, which I actually lost in an endgame. Yet I still wanted to know if I played the opening correctly.)