In the case of bolts and arrows, is it a fixed damage die or does it depend on the weapon used to fire the bolt or arrow?
Monk, PHB. pg. 78 under Deflect Missiles
If you're asking about the Monk's ability with respect to catching and throwing it back at them, it uses the weapon's own damage dice OR the monk's damage dice.
It can do this since the caught weapon becomes a "monk weapon" for the return attack, and regardless of what it is, you can substitute the damage out with your monk damage. This text is located under Martial Arts (same page.)
You can roll a d4 in place of the normal damage of your unarmed strike or monk weapon. This die changes as you gain monk levels, as shown in the Martial Arts column of the Monk table.