If I have a unit on Abandoned Hall, I then cast Challenge on my unit and one of my opponents' units. Will my unit get the buff from Abandoned Hall before Challenge damage resolves?

No. The unit will not receive the +1 Might from Abandoned Hall before Challenge resolves.

Here's the sequence:

1. You play Challenge, choosing your unit and an enemy unit. Challenge goes on the chain.
2. After reactions, Challenge resolves — both units deal damage to each other using their current Might values at that moment.
3. After Challenge finishes resolving, Abandoned Hall's "when a player plays a spell" trigger is placed on the chain.

So by the time the buff would apply, the damage has already happened. And if your unit died during Challenge's resolution, it's no longer on the board to receive the buff at all.