The word Cuba comes from the Taino word Caobana. The Spanish named the island Juana, but everyone called it Cuba.
The etymology of the origin of Cuba is often debated. Most agree that it comes from the Taino language and it's definition being "where the fertile land is abundant". It seems no one knows for sure.
Cuba is a Republic, and if you mean country, then yes.
Cuba is an Island in the Atlantic Ocean near the Carribean Sea and also close to the Gulf of Mexico. It is also very close to the tip of Florida
Yes, they are the same thing. Nation is more commonly used in the USA.