mistake in puzzle http://en.lichess.org/training/31095 ?

In puzzle http://en.lichess.org/training/31095 the best move as move 2 isn't to threat king with bishop in order to prevent him from 0-0-0 and then eat ?

Giving away your bishop by 2...Ke7 and 3...Kxf7 only for preventing 3...0-0-0 doesn't sound like a very seductive move.

2. Be7 Ke7 3.Bc4+

So what? 4.Ke8 and we are at the beginning again.

Ok, I didn't see that exposed black queen. But still, after 2.Be7+ Kd8, if 3.Qxh8 then 3...Qc2 forks White bishop and rook, and if 3.Bb3 then 3...b5 and White rook is trapped. You lose material anyway.

dmpbcn no. If 3.QxRh8 and you play 3...Qc2 I could for instance just play 4.Na3 and after I guess you eat 4... QxRa4 I would play 5.Bb3 and later 6.QxNg8 and later 7.QxRa8. if 3.Bb3 and 3...b5 4.Rh4 threatening h7

Eh, no, after 1.Qg7 Nd7 2.Bf7+ Kd8 3.Qxh8 Qc2, 4. Na3 would be rather bad, since then 4...Qd1+ is mate in 2 :)

Bf7+ on move 2 is an inaccuracy, since you have to just play 3. Bb3 after Kd8 to stop Qc2, and then you're still winning, but it's much closer.

The puzzle's current solution is by far the cleanest :)