I love the top bloom - I've never seen one in person~ how nice!
They should do well in Florida in the full sun. Sometimes they surprise us in certain climate zones and come back as a perennial, but living in Arizona I have only had them come back for one year so far.
Portulaca, Moss Rose and Purslane are all members of the Portulaca family. Each is a different name for a variety of the species.
Your second photo is portulaca, the first and third are known as purslane.
You can read our other threads for great information describing some differences and look at photos in the plant database.
