Yes to the first, probably no to the second - timing out and walking out of the store would most likely be considered a quit. There is normally a procedure for asking for a transfer, and you would need to follow that procedure BEFORE timing out and walking out of the store. However, if you had been consistently paid less than minimum wage, you might have some sort of claim based on that. You need to talk to an employment attorney in your area. Since you were making less than minimum wage, you can also contact the US Department of Labor, wage and hour division. That's federal minimum wage however, and I believe that Florida's minimum wage is actually higher.
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Although you may have a minimum wage claim, the total amount of the wage loss appears to be less than $100. Even with liquidated damages the loss is under $200. thus, a question you have to ask is whether it is worth your time and expense to pursue such a small claim. If you decide that it is, your best bet will be to seek payment informally prior to filing suit and if that is not successful, file suit in Florida Small Claims Court under the Summary Procedure Rules. As far as a wrongful termination claim or any other claim related to the separation from employment, it does not appear likely that a viable claim could be brought based on the facts you have provided.