I have a quick question: What's the notation used to indicate that a certain part of a piece is supposed to be played at a higher/lower tempo but only during a repetition. For instance, if I have a D.C. al Fine at the end of my piece, and I wanted to play the entire piece 40BPM higher than the original tempo on the second run, how could I write it?
Just use text. I would put this information with the D.C. (or D.S.) marking and with the original tempo marking. But I would put it inside a bracket.
So for instance, at the beginning:
"Allegro (faster on D.C.)" or "Allegro (faster 2nd time)"
"D.C. al Coda (faster 2nd time)"
You could even write the actual change of tempo. For instance: "Allegro (Presto on D.C.)" or even put the different metronome markings in a similar fashion.
For these kind of distinctions, you can't beat just using text to explain what you want.