This line draws after 3...bxa4.

The black king should not move to the 2nd rank, therefore we can move the king.

(White text)

3.Kg7 Kd4 4.Kf6 Kc3 5.Ke5 b4 6.a4

Correct. What happens after 2...Kxc2 3. a4 b4 4. a5 Kxb3 5. a6 Kc2?

This is not a rook pawn, neither does taking it possibly result in stalemate.

Correct. The lesson for the beginner from this position is that to win, White must arrange for Black's pawn on the 7th rank to be a knight pawn, not a rook or bishop pawn.

(You could have saved some typing after the promotion by simply saying, And White has a book mate in 21.)

Before the 3rd move, White had a mate in 20 going. 3. Ba6+ makes the mate two moves longer. It wouldn't really matter, unless the stipulation had been White to play and mate in 20.

I’m not sure if all B+N vs P endgames are a win for the Bishop and knight...

I mean not the pawn on the second rank.

Not all are, but in this one, White to play can mate in 34.

La Bourdonnais' picnic

4. Kc4 draws.  4. Rd8+ wins easily.

True, but it could take a while. In your position, with White to move and best play by both sides, Black will mate in 39.

What would black do next to prolong mate?

All three of Black's legal moves draw. Does that count as prolonging mate?

Epaulette mate. Epaulettes are those shoulder-tabs worn with a uniform. The chess term comes from the arrangement of obstructing pieces, one on each of the mated King's "shoulders".

https://en.wikipedia.org/wiki/Epaulette

I like to put the black king at h2 and ask my friends if Black to play can win. They usually misguess it's a draw.

What is your favorite endgame position?

A winning one.