I've never done it, but IIRC, you need to dissolve your lye in water first, and then add the mud to the water. If you add the mud first, the lye won't dissolve. I assume you could also hold back a bit of your water, blend the mud with that, then add it at the end.
Yep- as the others have said, you can most definitely use it. I've used it once before in a salt bar batch in order to make my bars look like granite. I added it straight or 'as is' to my batter and lightly stirred it in right before pouring to give things a speckled look. They turned out really cool looking.
I've used dead sea mud with no problems in CP and CPOP soap. Like dixiedragon suggested, I add it at the end in a bit of water. Though the idea is lovely, it's dead sea salts that cause problems in salt soaps.