Looked on the faq and couldn't find anything on this
1.In the Slayer action it references a quick action what is it?
3. When full moon is drawn does the card stay out for the entire roundirectory so the new monsters added gain its effect?
Quick cards were in 1st Edition and the concept was flipped around for 2nd Edition. In 1st Ed Quick cards were cards that you could play any number of, while the other actions were 1/round.
Treat it as saying "non-[Epic Sun Symbol]" instead of Quick.
The Full Moon does stay in play for the round.