The general rule in Florida is that employment is "at will" absent an express agreement to the contrary. At will employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true.
Policies that an employer may implement generally do not change the rule of at will employment. This is to say, even if an employee can prove that they didn't violate a policy, or that the policy required discipline prior to termination, that would not make termination illegal. Courts generally regard employer policies as mere guidelines offered by the employer as a courtesy to give employees a general idea what to expect--nothing more. With rare exception, an employer cannot be sued for violating its own policies.
So, at this point, to be candid, your employer has already done several things that they were not legally required to do. No law in Florida entitles private sector employees to review their personnel file, but your employer did. Likewise, no law would have required your employer to reconsider its decision to terminate, but yours did and has reinstated you. You actually did not have a right to either of these things.
Now, at this point, your employment is likely on somewhat tenuous grounds. So, typically, you will want to cooperate with your employer as much as possible. Again, keep in mind that when it comes to signing policies, writeups, etc. NONE of this generally stops your employer from still terminating you at will. So, it's not as though by not signing you are somehow gaining protection. In fact, not signing may very well result in your termination, and that too would be perfectly legal.
The simplest way to look at it is this: employment is a voluntary relationship between two parties. Either can terminate the relationship at any time for just about any reason. So, your only real job protection is to make your employer want to continue employing you. Certainly, you should not sign something that is untrue or which you strongly disagree with, but keep in mind that by refusing you may be compromising your employer's desire to continue employing you. Ultimately, you and your employer have to reach an understanding as to acceptable terms of employment moving forward.
If I can clarify anything at all for you, please do not hesitate to ask. It is my pleasure to assist you further if necessary....