Welcome to FL USA

Where in FL USA can one legally purchase fully automatic weapons without a special federal permit?

Just about any federal dealer. There is no permit required to purchase fully automatic weapons in the United States; you just have to pay a transfer tax. Unfortunately processing the tax payment takes about a year, in their effort to turn it into a form of permit, but that's not what it is. Anyone (without criminal background) can pay the tax and buy one.

There is a ban on the import and manufacture of new ones (for civilian use) in place since 1986, so the ones available for purchase (by anyone, again, no "special federal permit" required) cost about 10-20x more than they would cost otherwise, which effectively restricts them to "rich people only".

They're freely available, though.

You have to pay $200 and send an application to the Bureau of Tobacco and Firearms. It takes 8 months to a year; they will do a background investigation and send you an approval form if you pass. Then you can purchase the (used) machine gun. Fully automatic weapons are not currently manufactured in the U.S.

Florida, in particular, has banned machine guns like the AK-47 which is to say weapons that fire multiple bullets with one pull of the trigger.

Semi-autos are the dominant technology in firearms; when a bullet is fired, the energy released forces a fresh bullet into the chamber, ready to fire but you must pull the trigger again. This is known as "semi-automatic" and is legal everywhere, for now.

How difficult is it for a person to modify a stem-automatic weapon to make an illegal fully-automatic?

Up until the Vegas shooter in October 2017, you could add a mechanism called a bump stock to a standard semi-auto AR and make it shoot continuously like a machine gun. The Trump Administration banned the device (angering quite a few of his base). Is it difficult today? Not for someone who has some knowledge and connections. The how-to videos and files are still floating around. It's not recommended, obviously, because it's now an illegal modification, but there are thousands of them already out there and it's likely people are still making them in garage workshops.

You don't need connections, it can be done with a simple metal coathanger and pliers in 20 minutes. There are instruction videos on YouTube.

It's a federal felony, however, good for the better part of a decade in jail.

> Fully automatic weapons are not currently manufactured in the U.S.

This is a false statement. Only manufacture of automatic weapons for civilians is banned in the US.

Many automatic weapons are manufactured in the US for police/military/law enforcement.