I try not to get the scales wet, but they always seem to get a little water on them.

Rinse of the blade, do a light strop on my towel to dry it off, then strop 10/10 on my linen/leather to get any moisture/goop off the edge of the razor.

As for the brush, I just rinse it well and flick it dry and let it stand on the shelf to dry the rest of the way.