@@@Not in the UK sense but you have county/city tax stamps.
Please link to one in Florida (OP's destination).

@@@Closing on a house involves buyer, seller, real estate agents, closing agent or attorney.
An attorney is unusual in Florida, especially for private real estate. The contract is usually done by the real estate agents (and included in their fee), and the closing is done by the escrow/title company. This is different from the UK where an attorney is almost always in the process.

@@@Should your agent be buyers' and sellers' agent he will go over a number of disclosures with you and a binding contract of all three parties will be signed.
It's called double dipping, and makes the slender fiduciary duty the agent owes you under law even more tenuous. How can the agent work on your behalf if s/he is also working for the other party? Enter at your peril!

@@@Registration fees vary from county to county.
Yep -- in the order of 10s of bucks!

@@@You do not have to have title search/insurance. Personally - I would highly recommend it as it traces ownership and liens on the property.
You'd be crazy not to have a title search!!

@@@What do you mean by penalty for selling? Yes, homestead excemption does not apply for tax purposes.
The seller does not benefit from many of the tax write offs citizens and/or permanent residents have when the property is disposed of. For this purpose, 10% of the sales price is withheld when s/he sells, reclaimable only after selling up with Uncle Sam.