Which openings for white and black lead to the fastest games and which lead to the slowest?

The fastest games usually come from the openings in bullet games... and the slowest games usually come from the openings in correspondence games...
Serious answer, you're much more likely to have a 'slower' game by playing a closed system such as the KIA, London, Tarrasch, or Closed Sicilian as White, where Black can equalize but neither side can prove an advantage out of the opening, or by playing a hypermodern system as Black, where White can prove an advantage out of the opening with accurate play but there's still a game of chess to be played afterwards.

Who cares?

There is no answer to this.  I have seen every opening go under 20 moves in some games and over 100 in others.

I won as Black in a Colle System (a line that stereotypers would say is slow) in 16 moves over the board.  I have seen the Latvian Gambit go over 100.

Give it up - not the way to be thinking in chess!

Obviously the Exchange French, Berlin, and Petrov are the slowest. Even if the game only lasts 10 moves long, it feels like an eternity!

I am not a fan of slow games myself so I stay engaged by seeking interesting middle games where there is imbalance and counter play; time flies when you are having fun!

Ironically, my rapid games have less moves compared to blitz or bullet play. That’s a whole different story altogether.