When you Punish a demon how long does it take a demon to recover?

Use the damage rules; also see the rules for demon's Stamina and Ability use. [1]

Can you perform compounded punishment? For instance, you can automatically punish your own bound demon and remove up to your Will from its Power; can you let it rest and then punish it again a few days later and lower it's power again?

That is certainly possible. It's also a good way to guarantee a mortal enemy. [2]

Using Punish on a Demon actually lowers the demon's Power score temporarily, rather than penalizing it as per the physical damage rules. This is a significant difference when considering Humanity Gain rolls that come as a result of a successful banishment. (See Banish Ritual)

For clarification: Punishing the demon lowers its Power and all associated supernatural powers. It does not penalize the demon's Stamina, Will, or Lore, except insofar as successes on the Punishment ritual could be rolled over into other conflicts, per the usual rules.