What are the quckest helpmates delivered by the rook, knight, bishop, and pawn?

Question

What are the quickest helpmates, which is where both sides help administer checkmate to one side, delivered by the rook, knight, bishop, and pawn? The said piece has to deliver the checkmate on the final move.

Answer 1

Here's what I came up with.

Bishop took me 3 moves:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1.e4 f5 2.Be2 g5 3.Bh5#  *

Knight took me 3 moves as Black:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1.e4 Nc6 2.Ne2 Nd4 3.g3 Nf3#  *

Pawn took me 5 moves:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1.e4 Na6 2.Bc4 Nb4 3.e5 Na6 4.e6 Nc5 5.exf7#  *

Rook initially took me 6 moves, with 1.h4 f5 2.Rh3 f4 3.d4 f3 4.Rxf3 g6 5.Bh6 Nc6 6.Rxf8#. But I found a quicker way to checkmate with a rook - promote to one! This results in a checkmate in 5:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. g4 Nh6 2. g5 g6 3. gxh6 Bg7 4. hxg7 Na6 5. gxh8=R#

Answer 2

I came across a rook mate in 4.5 moves without promotion on a page called "Shortest Mates in Proof Games" at janko.at/Retros/index.htm. This elected curiosity for other types of shortest mates, including a shorter pawn mate than the accepted answer.

Non-Promoted Rook

[FEN ""]

1. a4 c5 2. a5 Qxa5 3. Rxa5 c4 4. Rc5 c3 5. Rxc8#

Pawn

[FEN ""]

1. e3 e5 2. Ke2 Qh4 3. Kf3 f6 4. Be2 e4#

Pawns can also do double-steps. Nick's Mad Chess Blog provides one of many possible sequences.

[FEN ""]

1. c4 d6 2. Qb3 Kd7 3. e3 Kc6 4. Qxb7+ Kc5 5. d4#

Via Bishop Promotion

[FEN ""]

1. d4 g6 2. d5 Bh6 3. d6 Kf8 4. dxe7+ Kg7 5.Qd6 Qf8 6. exf8=B#

Via Knight Promotion

[FEN ""]

 1. h4 d5 2. h5 Nd7 3. h6 Ndf6 4. hxg7 Kd7 5. Rh6 Ne8 6. gxf8=N#

Another option is to promote, and then give mate.

With A Promoted Bishop

[FEN ""]

 1. d4 c5 2. dxc5 Qb6 3. c6 Nh6 4. cxb7 Nc6 5. bxc8=B Nd8 6. Bxd7# 

With A Promoted Knight

 [FEN ""]

 1. g4 Nc6 2. g5 e6 3. g6 Nce7 4. gxh7 g5 5. hxg8=N Rh3 6. Nf6#

With A Promoted Rook

[FEN ""]

1. g4 h5 2. gxh5 g6 3. h6 Bg7 4. hxg7 Nf6 5. gxh8=R+ Ng8 6. Rxg8#

Answer 3

It's not in your original question, but the game here can be adapted for a mate-in-5 by the king:

[FEN ""]

1. f3 e5 2. Kf2 Ke7 3. Kg3 d6 4. Kh4 Kf6 5. g3 Kg6#