Typically no. That would be quite difficult to safely remove the zoas and reattach to a new plug. I’d imagine these are ordered frags/shipped, which I would not want to add the extra stress after being shipped
Yes, I routinely remove corals from their plugs... sometimes I glue to a new plug, sometime just glue directly to the rock in tank. Zoas usually come off pretty easy.
I just let it sit in whatever it came in on. Don’t see the point in taking it off right away. Even if I were gonna mount them on rocks I’d wait a couple days make sure they open up and don’t melt.