Can I sue my previous employer for giving bad references about me?

Yes, there is a florida statute giving you the right to sue and making the employer pay your lawyer fees and court costs if he's found guilty. Keep in mind that this does not protect against opinions ("he is a bad employee") only against false statements of fact. If you want proof, have a friend call from an office phone pretending to be a prospective employer and see what they are saying about you.

Possibly yes. The difficult thing is proving the violations. Employers are smart if they only verify dates of employment and job title, but smaller companies may make mistakes.