You need to go to Discovery cove and get the swim with dolphin package. The price depends on which day you reserve, it's really a worthwhile experience.
You have to pay separately for swimming with the dolphins, and it's not at SeaWorld.
No you can't swim with them.
You can't swim with them, only pet them and feed them. The price is currently at 25$/person on their website, but its usually 45$
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