Well, I beat fish tycoon so now I'm onto this game...

Why does my ocean have an algae?? And how long doe it take for it to go away?

It's one of the puzzles you need to solve. It won't go away on its own. As with our other games, you can find a lot of help that's already posted here in the forums. If you do a search on "algae" (click on the Search link at the top of the forum list) you will find a lot of discussion and answers about that puzzle. There's also the VV2 Guide Section.

I have Level 3 on Farming, Engineering, Science, and Exploration. Supposedly, I should now be able to uncover the mosaic at the bottom right of the island (according to two sites I've gone to), but every time I drop someone there, it says "More research may be necessary". I'm working on getting 3rd Level Culture and Medicine. There is nothing else. Do I still need to do something else first?

You're on the right track and LadyCFII gave a great clue. Go here and read what it says for if you REALLY want to know.