Stockfish behind the scenes

My Duck Duck Go Foo must be off :)

When engines go at it head to head:

1) How is the opening selected. Is randomization involved?
2) How is the clock managed. I.e., is a human ever involved in a match?

1) Depends on the engine.
Stockfish (can, and usually) uses an opening book, and iirc has settings that determine how much it varies the opening.

2) A human is never involved in a match.
Stockfish uses a low amount of time if:
-The other side plays according to what stockfish believes is the best move, and then stockfish just plays what it calculated before
-If there is a forced mate

Otherwise, stockfish generally makes longer moves.
Stockfish usually makes longer moves when there is more time on the clock.