When playing as black is copying your opponentsevery move until they blunder a good tactic?

Trying to copy white's every move can be dangerous, especially if there are multiple pieces/pawns that are attacked at once, but in your case it worked.

Wouldn't recommend doing it against higher rated players though.

Yes it is a good scheme. An Issue can arise when the opponent plays a forcing move.
The Petrov is an example of a copy being very theoretical.
Queens Gambit is an example of copying being a bad play because pawn breaks are extremely forcing in a commitment type way.

If your opponent is playing lackadaisical chess then the move copying pattern can be disconcerting to them.
In most openings however copying for to long will lead to victory for the first player.

There is no way this strategy can possibly backfire.

HOLY CRAP WHY DIDN'T I THINK OF THIS I COULD DRAW MAGNUS

So you can do this until you find a moment that seems good to deviate, and then stop copying. The problem is, your opponent will have arrived at that point of deviation with a specific plan, potentially, while you have not. So the potential that you have overlooked something and have deviated too late is pretty high.

What is the fastest mate for white, if black does this?

Just try to copy Scholar‘s mate with 3.Qh5 instead of 3.Qf3...

You're right, that was a stupid question. :)

There must be a game between Capablanca playing white in an simultaneous exhibition and one of this opponents had the clever idea to copy what he was playing. In the end, Capablanca won. That is to say, copying is not going to achieve much for black.