Ball Lightning

Is the damage resolved one at a time, after each hit?

Yes! Resolve the damage (and any deathrites) from the first hit, then bounce for the second hit, resolving that damage, then bounce and resolve the third hit.

Can I hit the caster or other allies with this?

At the first location of the projectile's path, it cannot hit allies or the caster, even if it hits an enemy there first. If the Ball Lightning leaves the first location, it could bounce back and hit allies or the caster later in its path.

After bouncing off a unit, does the ball hit them again immediately since they are both at the same starting location?

No. But the ball can hit other units at that location after changing direction, bouncing back and forth.