Have you read Perelandra? In that book, there are floating islands similar to this, but they're not turtles. You may be able to pull some ideas from that if you do a google search on it. As far as the turtle idea goes, it sounds like you've made a really good start.
Waith regard to the "how would it feed without diving?" question, the Portugese Man O'War is a creature that lives entirely at surface level, and uses trailing tentacles to catch prey. Something else this tangentally reminded me of was the game Subnautica, where you bump into harmless blob-like undersea creatures called Floaters, which attach to things and float them to the surface. Later on, Spoiler you find a full-sized island which is unconnected to the sea floor, instead held aloft entirely by a colony of giant, ancient floaters attached to the underside.
