From what I understand about Rain effects (ie normal Rain), the Status effect is applied each turn refreshing its duration. The duration of the Status effect depends on how its defined in the Potion.txt file- I believe Wet is normally set for 5 turns.
Regarding the enemies getting the new skills; it would be too much work honestly for little payoff, and involve replacing Global character templates with one that points towards a Script that uses the new skill instead of the old one. I haven't worked out how to replace a Global character template yet, since those aren't like normal RootTemplates.
From what I have seen about the damage from summons, I think it scales with their level. My spider's Acid Breath listed low damage in its tooltip box when I tested it out.
