You likely have zero case against the "Karen" and for good reason, coming from someone who owns several guns of my own. Don't talk about that shit at work. Don't talk about that shit unless you 100% know the people around you period. People are well within their rights to label you as someone to be conscious of the moment you do, because even if you work in a gun friendly area, talking about it outside of specifically gun oriented leisure places where you are not working and/or helping a customer is a red flag (not the gun control type) for non-owners. It makes it seem like it's a large part of your life, whether it is or not, because for a lot of people who talk about them in public, it is.
During a mass shooting scare, red flags mean a lot, no matter how innocent it was meant. You cannot control people's perceptions of you, nor are you likely to gauge how people perceive you accurately. Everything she stated was fact, as confirmed by you, derived opinion from her perspective, and that is why you very likely have no hope of suing her. Slander has to be intentional lies to ruin your reputation. Unless you have documentation about harassment from her in the past, don't expect anything to come from lawyering up against her, though you are likewise within your rights to try.
Now, different situation, your company. This is likely a case of them covering their asses and reputation, because whether you like it or not, how you have been perceived is something they very well might want to distance themselves from. Get a lawyer to protect yourself specifically to avoid misstepping into legal trouble, as while they have quite possibly overstepped by a large margin here, you are very much in potential legal trouble territory. Get a lawyer now, and regardless of how you felt before than, I would recommend being prepared to find a new job as you likely will not be perceived the same way after this long of an investigation, though again, do not do anything beyond this point without a lawyer's guidance.
On top of all this, remove this post, as you have stated several details that very well might be used against you in a lawsuit.