Sweat spots are showing up in after staining, can they be fixed? How can they be prevented?

a Hat or headband and a little a/c will go along way. You have popped the grain with the beads if sweat are left to dry. If you wipe them up as you see them they will usually be unnoticeable.

remove the work from eh job.Use a buffer to apply the stain..bandanas or head bands as Kevin suggested.
to fix them just rub them out with fine paper and reapply stain.

are you getting white spots? as that happens during the application and stain is wet.
if they are darker then they are in the floor before the stain and grain is raised.
either way the fix is the same.