I used pumice rock in a FW tank but I wouldnt use it in a SW tank. The other post are correct that it leaches into the tank. I had algae problems and also the rock is very sharp and could cut your fish.
I used a very large pice of pumice as the ONLY rock in a 60g cube for 22 years without issue. Using a couple large spade bits and my drill I turned it into a cave with lots of swim through's and places for fish to hide. I was able to keep pretty much anything I wanted with the exception of acropora sp, but that was more because of the lighting than anything else
Yes, it floated at first, much to my surprise! A generous helping of silicone on the bottom did the trick just fine.
I would be more concerned about the pumice abrading the eel's skin as it swims around.