1. I don't see why not. Water is water. If there is any microbial life in the water, it should transfer those microbes to the new batch of charcoal, which is the goal. If not (no microbes in the water), at least there shouldn't be any chlorine in the water which would kill microbes in the
compost that you add.
2. This is just my opinion, but I don't see anywhere in nature where foliar sprays naturally occur. If permaculture is a design science that mimics nature, I don't think you're not going to find anything like that in a natural setting. But you can always water your plant with that water.
Best of luck.
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf