Learn Italian: Scusi, chi aspetta? - Excuse me, who are you waiting for?

The Italian verb aspettare means 'to wait for'. Because the 'for' is already built into the action, you don't need an extra preposition like per. You are simply asking 'Whom do you await?'.

Does chi mean 'who' or 'whom' here?

It acts as 'whom' here, but the great news for learners is that chi never changes its form! Whether you mean 'who' (the person doing the action) or 'whom' (the person receiving the action), you always just use chi.

Why does the verb aspetta end in -a? Doesn't that mean 'he/she waits'?

Yes, aspetta is the 'he/she' form of the verb. However, Italian uses the 'he/she' form for the formal 'you'. Because the sentence starts with the formal Scusi (Excuse me), we know the speaker is politely addressing a stranger, so they use the formal 'you' verb form.

If I wanted to ask a friend who they are waiting for, how would this sentence change?

You would change both parts to their informal 'you' versions. Scusi becomes Scusa, and aspetta becomes aspetti. The informal question to a friend would be: Scusa, chi aspetti?