We have never used it for wet grinding nor made any paste with this grinder. We bought this twice from Amazon and both the time it worked only for few days and then died. So not sure this perticular product of Cuisinart is really came out to be bad for us.
I haven't tried adding liquids, but I bet you can add a few drops of liquid or oil. But don't think of this as a mini food processor, it's very small capacity. Mine still works, but the blades got dull after about a year. That's my only complaint.
I would think so. I used it mostly to make my vegan parmesean with almonds and miso paste. Obviously, miso paste isnt water but its the same principle. The oils in the nuts will make it into a paste. What are you looking to grind? If u like ill try it and see if it works.