The only character I've seen available for pictures is Nemo. He appears outside the Living Seas at the coral display. There is a Nemo & Friends display of real fish inside LS
Shaker's the bear on the left. He's from the Country Bear Jamboree.
Nemo is the only character from the film that does meet-and-greets. He's usually accompanied by a couple of stilt walkers dressed as coral reefs though. Inside the Living Seas, there's a show called "Turle Talk" where Crush virtually interacts with the audience. It's not a meet-and-greet per se (no autographs and photos are tough since he's on a screen), but if you like Nemo I'd say it's a must-do to be able to meet Crush.
If you like Nemo you should definietly see Turtle Talk with Crush inside the living seas. He will talk to your kids and they will have a blast! Have fun