I have 3 scuba divers in the family and they've never found a bottle by scuba diving. Instead, the lifeguard sim is the one who finds them on the beach he usually gets sent to. It's off to the side of the screen near the bushes. That said, he's found a few bottles, but none of them have had readable messages inside unless I've done something wrong. He just picks them up and puts them in inventory, like any other collectable object. There was then a mission to turn them in so he did. I never saw what the messages said.
Regarding the uncharted islands... I've got 3 of them so far, one came from running a 5-star resort, another came from diving and exploring a cave (I believe it was either Davy Jones' Locker or Mermaid Grotto), it just through me up there on an island where a bunch of other scuba divers stood and a few minutes later a boat came and took me to another island and said I'd discovered it. I think that one was called Beryl Shores. the one I got for being a 5-star resort is called No trouble Atoll. And I don't recall the name of the one I got for putting together the 4 map pieces I collected while diving and opening treasure chests... that one opened up near a chain of islands that are mostly flat, with no stand out features.