So, when I'm calculating the saves of a 1st level Solarian's revelation saves (say, to avoid Supernova), the formula is (level X 0.5) + CHA bonus. Is there a minimum of 1, as there is when calculating Resolve, or does it round down to zero? Would a CHA 10 Solarian have a save DC of 10, or 11?
Round down. Things in this system always round down unless there is a specific exception called out.
The 10 CHA level 1 solarian would have DC 10.