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#1, yeah, stones are notorious for that. Prolly not so well known to you folks here, but the tool folks are well aware of it since they usually use stones in sheds/garages/workshops that may not be...

The Naniwa, rinse, wipe it down with a towel/cloth. Leave it out overnight somewhere dry and cool to make sure it's dry then do whatever works best for you. No heat, you'll make a mess of the stone...

What brand/type are they?

Some don't care what you do to them, some require a little care and consideration, some need kid gloves.

Generally, let them dry, put them somewhere safe and covered...