I see this a lot, the best way I think would be to play for d5, but before playing it I recommend playing a6, Nc6, e6, and Nge7 or Nf6
How to respond to 1. e4 c5 2. Bc4

Let me try this again.
B20: The Sicilian Defense - Bowlder Attack. 1.e4 c5 2.Bc4.
The next move is 2...e6, prevents a common mate attack by targeting the f7 pawn.
What usually happens after that? Am I supposed to move d5 soon?
1.e4 c5
2.Bc4 e6
Then if...
3.Nc3, then 3...a6, intending a timely ...b5, and a game of queenside expansion.
Or if...
3.Nf3 or anything else that doesn't blunder a piece and give you an even better option, then 3...d5. Followed by classical development, when the tempo gained by attacking the bishop equalizes instantly.

After 3.Qf3 black plays Nc6, like this. Only a patzer would play Nxe4.
I agree. That's why I placed ?? after Nxe4. I don't feel that Nf6 stops White's initiative as well as 2...e6.
3.Qf3 would be a mistake as well, and the experienced player would notice it and play 3...Nc6. This would give Black a slight advantage. However, after 2...Nf6 3.e5, it gets tricky and Black must fight for equality, when the simple solution would be to play 2...e6.

5. Bxd7+ would be a mistake. Better would be 5. Be2. Why give up the bishop pair so quickly? Also, it does give Black the chance to lead in development.

I know e6 is the most simple solution, no doubt the best move in the position. But I like to try and make things go crazy.
In Blitz, it would burn some time on the clock for someone who has not seen the trick of 2...Nf6.

I would wait with e6. If white will really attack f7 later with Qb3 or Ng5 or something like that, then play e6.
Natural is 1.e4 c5 2. Bc4 Nc6 - preventing e5 and preparing Nf6. Even after Nf3 it is possible to play Nf6 or you can just go d6 or e6. Its not a critical line.

What would be the correct response to 1.e4 c5 2.Bc4 e6 3.e5 ?
d6 is just fine. d5 also make sense.

What about this.
Hello,
I'm not that great of a chess player, and lately a lot of the times when I've gone with the Sicilian I've seen an early bishop to c4, second and sometimes third move. I'm just looking for suggestions on how to respond to this, especially ones that would get rid of a Ng5 threat with bishop and knight eyeing f7. Also, someone earlier I played moved c3, to get the queen on b2. How should I respond to that? Thanks in advance for any help.