Puzzle of the week #262

Level: 
3-Bishop
Chess Diagram: 

[Event "Puzzle #262"][Date "2014.10.26"][Result "1-0"]1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4 Bxb4 5.c3 Ba5 6.O-O Nf6 7.d4 exd4 8.Ba3 d6 9.e5 dxe5 10.Qb3 Qd7 11.Re1 Qf5 12.Bb5 Nd7 13.Qd5 Bxc3 14.Nxc3 dxc3 15.Nxe5 Ne7

The 1st World Chess Champion has embraced and used this opening in his games like this one from 1862. White has managed to position all but one of his pieces in attacking positions. Black has not yet castled, but hopes to do so even at the cost of one piece. Your tasks:
a) Name the opening
b) Why can black consider sacrificing a piece in order to castle?
c) White cannot wait any longer and should attack; play the best line you can think of

Total available points for this puzzle is 20. The answers will be published next week together with puzzle #263.

Puzzle #261 solution:
Game: Diener - Dreyer, 1934. Your answers would have been better if more could have observed that after 8.e3! ... white wins a piece. This is a good example for all on how you need to pay attention at any moment in the game no matter how early it might be.
a) Nimzovich defence
b and c) The best lines:

[Event "Puzzle #261"][Date "2014.10.12"][Result "1-0"]1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Qb3 c5 5.a3 Qa5 6.Bd2 Nc6 7.Qd1 Nxd4 {Solution} 8.axb4 (8.e3 Bxc3 9.Bxc3 Qc7 10.exd4 {White is up a piece}) Qxa1 9.Qxa1 Nc2+ 10.Kd1 Nxa1

Correct solutions:
Bradley - 20 points
Brandon, Oliver, Coco - 18 points
Daniel, Cody, Jalen - 15 points
Hyson, Yakov - 12 points
Benjamin, Aaron, Dheera, Anya - 6 points

Standings:
Bradley - 42 points
Jalen - 33 points
Yakov - 32 points
Brandon, Oliver - 31 points
Hyson, Daniel - 29 points
Coco - 26 points
Anya - 24 points
Cody - 23 points
Benjamin - 22 points
Aaron - 9 point
Dheera - 7 points
Deryk - 1 point

Comment: 

Evans gambit