I'm not sure if they're allowed, but no one said anything to my son when he wore his on two different trips, and they were bright yellow SpongeBob floaties!
i wouldn't think any pool allows fins - public pools tend to hate them.
it's the mask where your nose is covered that confuses me.
i scuba dive (well used to before getting married) and often swim with my mask even without a snorkel. i don't really see a difference in goggles or mask as far as anyone else is concerned -