If I make payment in full of the demand by a collection agency/law firm, do I retain my right to file a FDCPA claim?

In deciding how to handle the defense of a collection case and how to assert an FDCPA claim, you should not rely on what someone without all the facts and documents says. That includes me and everyone else that offers her or his off-the-cuff opinions on the internet. So the answer to your question is that "it depends." While generally the FDCPA claim is seen as separate and distinct from the collection action, the case law is a little muddy. And it is further complicated by the possibility that the FDCPA issues can be brought separately in federal court while the collection action sits in state court. (There are several ways to put your FDCPA cases into court, which has to be decided on a consideration of all your issues.) But it seems to me that the more fundamental question is "why would you want to pay good money for defensible issues like usury or unreasonable attorney fees?" (I understand that there may be factors that motivate someone to make payments that they don't think is fair or lawful.) But this just serves to further point out that you should make your decision in conjunction with experienced counsel.

Under previously decided case law interpreting the FDCPA in the 11th Circuit, there are some violations by the debt collector in the fact pattern you have set out. Go consult with a local attorney that handles FDCPA claims. You can be awarded statutory damages and attorney's fees for each violation of the FDCPA.

Believing you have a claim and proving it in court are VASTLY different things. Lawsuits are about facts, not law. You still have to prove the facts that justify your supposed legal position. You are conflating a couple issues. Although what you state might give rise to FDCPA claims, the threshold issue is whether you owe the additional amounts. You seem to want to challenge your liability to pay the attorney fees and additional interest...that is a very different issue than an FDCPA claim. As such, if you pay the full amount, you have conceded that point as to the validity of the amount claimed to be due...at the very least, the fact that you paid the claim would be used against you. If you want to pursue this, retain counsel. If you truly have a viable FDCPA claim, experienced FDCPA attorneys would not charge you anything upfront and would collect from the settlement or judgement and the attorney fee provisions contained in FDCPA. A good litmus test for your claim is to shop it around to attorneys, if no attorney will take the case for no upfront fee, that is a good indicator that you DO NOT have a good case.