I've been meaning to get one of these for a friend. I would be very surprised if you couldn't just drain it, pop the head out, wash and dry it all, swap in a new head and keep on rockin' and when the washed head dries you could probably use it again.
Water isn't going to hurt it. Just open it up and rinse it out with water and let dry. Probably replace the coil if water got inside of the tank and saturated the wick.
If you are using rba just replace the wick.
I always rinse my mini with water when I clean it.
Again, I don't have one yet but watching rip do it it looks pretty standard. Over the sink I would just take it to bits like rip shows here and wash it and dry it and swap in a new head while the old one dries.
I wouldn't replace the coil if it got wet, just rinse it out with clean water and let it dry completely and it'll be fine. Same goes for the rest of the tank, just rinse it out and let it dry.
I wash my two Sub Tank Minis all the time. As far as the base? Open the air vent wide open and blow into the top opening. That forces a lot of the accumulated water out. Then let it dry.