Link

Here is a link that might be useful: Florida Gardening Forum - cross post

That's a beauty, but I don't know what it is.
Here's the website for a local palm grower here in San Diego county who's very knowledgable and helpful. Tons of pictures and info on his site, but if you don't see it, shoot him an email and ask. I'm sure he'll have an answer for you...and then let us know!
http://www.junglemusic.net/

Looks like a Livistona. Might even be the cheap Livistona chinensis you find at Walmart. They're slow in the sun but some folks say they're pretty fast in shade as they try to find light. Interesting assortment of plants. I don't know where you'd generally see them all growing together, since Live Oak and Liriope is more popular up north way.

Looks like saw palmetto or cabbage palm.

I'd go with Chinese fan palm (Livistona chinensis).

I have a big potted specimen I just lugged back indoors after the temperennial season. It does fine in light shade.