You are probably right about the flat things being nudibranchs. I remember shaking lots of them out of seaweed last year in Port A. They do swim in the water by "flapping" their sides.
As far as the anemones .. well, it is a risk. You need to read the posts by our sponsor coordinator Mark, and his adventures with a carpet anemone and all the victims it claimed. Now, rock anemones do not have as strong a sting as carpets, but I think they are pretty powerful.