How new? They may still be getting used to the new tank, you can also try moving them and leaving them a few days until you find a place they are happy
I was thinking that the white fuzz looked w bit like nudibranche eggs. But considering these are palythoas and not zoas I feel like it’s probably something else. Maybe they are still acclimating.
The white patch on the left hand side is a sponge. They are fine just watch if it starts trying to grow over the zoa and if so they are easy to remove with a pair of tweezers. It looks like they are collecting some debris on the tissue and will probably open up in a area with more flow. If they do not open in more flow a furan 2 dip will help. One pack of furan 2 to one cup of tank water for 10 min once a day for three days and place back in tank in an area of high flow