Absolutely. Florida is a very employer friendly state. They can fire you for just about anything they want to, including they don't like your socks. But don't discuss it, deny it if the situation is questioned by the employer, stop talking about the whole dramatic thing with your co-workers, and just do your job.
Yes, they can, if they feel like it, they can, but don't push it and it will likely die, in other words. By the way, if it's an issue, don't date your co-workers. If you decide you're going to date, one of you should find another job.