I would like to provide a Ethereum node in the State of Florida in the USA. How many Ethereum nodes are already on-line in Florida? How do I go about buying and registering a new Ethereum node?
You don't need to buy or register an Ethereum node. You can simply download one of the clients such as go-ethereum and run it on a computer connected to the network.
Ethereum nodes will automatically connect to other nodes and synchronize a copy of the Ethereum blockchain, so there's no formal registration needed.
If you want to stand up a mining node, that will require some advanced setup. Either way, I'd highly recommend you read through Ethereum's documentation before you get started.