Thank you for your information and your question, although I am not exactly sure what rights you are asking about since that is a very broad question. I will cover the basic issues and if you have a specific question, you can ask it in a follow up.
First and foremost, Florida and Georgia law, as with most states, are virtually identical in regards ***** ***** relevant issues you raised. Unless you have a specific term contract that lays out all of the terms and conditions of employment and only allows for termination for "cause," then you are considered an "at will" employee. Also, unless you have that same contract that says the laws of Florida apply to a dispute, the law of Georgia would apply. Again though, that issue is moot since they are the same type laws in both states. This goes for wages, discrimination, etc. The appointment letter is not a term contract unless it says it is, so all of those terms and conditions can be changed prospectively.
So, assuming you don't have that contract I mentioned and are "at will" your employer can let you go for any, or no, reason and with no notice or warning unless doing so is motivated by your gender, race, national origin, age (over 40), disability, religion, pregnancy or military service.
Neither State, nor Federal law, requires that an employer pay out any accrued unpaid vacation upon termination unless there is a contract that says it will be. Then it becomes a contract issue and not a wage law issue if there is a contract.
Again, please feel free to ask follow up questions if you have them. If none, then if you could take a moment to let me know I covered your questions and also to leave a positive rating of my efforts to explain the law of your issue to you, then the Site will give me credit for assisting you today. Thank you