Does this apply to common law relationships?
I believe you are talking about is a common-law MARRIAGE. What I'm going to write below is entirely dependent on what the law is in your state. It may or MAY NOT be accurate as a generality.
First, if your state recognizes marriage by common-law, it may or may not exist in your case - you (or she) can't just say it's a common-law marriage; there are elements that must be satisfied for one to exist, for instance in some states, a "holding out", meaning that you must represent yourselves to the public as husband and wife, and probably for a set number of years.
Second, the issue of common-law marriage just goes to whether or not y'all really are or are not married, and not as much, if at all, to IF there is a marriage how it will be dissolved. In other words, depending on what your state's law says, the "common-law" issue is whether y'all are even married in the first place. If it turns out y'all are, THEN you go to the next issue, which is dissolving it (e.g.: the divorce).
What happens if a prenup is signed?
It depends on whether or not you are married, what the prenuptual agreement says, and whether any action on your part or parts during the marriage has changed what you agreed to in the prenup.
I've only been here a short while, 1man, and I continue to be happy at how eager and willing folks here a re to give advice. I've learned a lot in the short time I've been here. BUT! ...
... I am telling you, do NOT rely on what I or anyone else says here. Divorce is a matter of state law, and each state's law is different. Also, the application of that law to the facts of your particular situation will UNDOUBTEDLY heavily influence your legal position and what you decide to do.
I cannot stress strongly enough to you that you contact a lawyer in your own state who specializes in domestic-relations work. That is the only ... the ONLY ... way that you can get an answer that you can rely on. If money is an issue, all state bar associations that I am aware of have a separate lawyer-referral service to get you to the right person, and they can often handle cases "pro bono", meaning without charge.
Keep this in mind, in some states if there is a Personal Protection Order [PPO] filed against you, ...
DAMN right! WHATEVER you do, don't get physical or do anything that could support a request on her part that the court enjoin you!
A final personal note: I feel for you, man. I have gone through a divorce, and while the good folks here and elsewhere can empathize, they cannot truly sympathize with you unless they've gone through it too. So, here's the second piece of good advice I can give you about this:
The biggest single source of the worry I can tell you are feeling right now is being caused by your not having the hard facts anyone has to have to make a decision on anything. Using the matter of your guns as a specific example, your worry stems from the fact that you are asking "What if?" and "Can she?" Until you have the answer to those questions - and I mean definite answers, not a concensus of folks who are on your side but are not representing you as professionals (meaning a lawyer in your own state), you will continue to worry. The sooner you move ahead and contact a lawyer in your state, the sooner you'll get some of the worry off your shoulders. So, don't delay - contact a lawyer, and get your answers, and then you'll find that you are in a much better mental position to proceed.
A final thing that helped me: think about it like this - you are currently walking through thick woods. Try to remember that there is an edge to the woods, and you are going to get there by doing what you're doing - continuing to take one step at a time.
So proceed - and the first step is to contact a domestic-relations attorney in your own state.
Hang in there, bro.