I don't believe that it moves of it own acord, I believe that it will let its self become unatached from an object and then let the curent do the moving. It looks like it has a little hole on its top when it is in a low curent location and lost of light it get little bubbles on top not like a anemone sort of like a fox coral I believe thet are called.
It is very small shaped like a scone or tea bisket. I was prity sure that the second pic was snail eggs but the one that would come up on a net surch were of a glutinous mass with eggs in it. I also have some of these glutinous masses in the tank I am keeping an eye on them. I have boughten 3 different types of snails but have seen about 7 different types now they are almost all grasers there is some tonga snails I believe they only come out when dark or inot shadows. I am not much of an aqua skaper but I do have alot of caves and nooks for fish to swim in and through.

Bill