are you allowed to show up armed, in case they are waiting for you? If you end up in a shootout, will you be considered the aggressor? Seems dangerous to me
In America? Yes. I can't speak for other countries. If you do get in a shootout, well, that's likely self defense.
Many will wring their hands over taking direct action, but I can speak from experience, the police and legal system don't give a damn about you or your possessions. I would absolutely be willing to risk it rather than go through the hassle of buying a new car right now.
People wildly overestimate how quickly most people, criminals included, are willing to get into shootouts or even initiate violence against someone they don't size up as a victim.
If you show up to retrieve your stolen property chances are 99 out of 100 times you'll get it handed back without much of a question. They are just as scared as you randomly showing up and tracking them down as you are of them. You are not acting the part, and your actions are dangerous and abnormal - even most predators pause in such situations, and most criminals are not predators but opportunists.
Most cases. Obviously it's not the safest thing in the world, and if you're not comfortable with confrontation I wouldn't recommend it.
I'm financially well off enough now where I'd likely let pretty much all my physical possessions walk without recourse (what will happen if you just report to police). It's not worth the risk:reward benefit any longer.
However there were times in my life where I absolutely took matters into my own hands and collected stolen property that was critical to my livelihood and too expensive to replace. It was surprisingly easy every time. There were times way in my past I would have defended certain property with my life if it came to it, since losing it was nearly the same thing.
> are you allowed to show up armed, in case they are waiting for you
Every US state has slightly different laws about open carry and concealed carry laws in public. They also have different rules about self-defense.
There was a case recently where a guy sat in his own garage with a shotgun (due to some recent burglaries) and shot an intruder. He was charged with murder. I think because 1) it was pre-meditated (he expected an intruder and intended to kill them), 2) his life was not in imminent danger (the intruder had no weapons) 3) he made no attempt to de-escalate the situation and did not fire a warning shot or tell the person to leave.
I think California is like this where you are obligated to not be the aggressor, even on your own property, and must make attempts at a non-lethal de-escalation if your life is not in immediate danger. But then there are states where you can "stand your ground" in public and defend your property with lethal force. So, it all depends on local laws.
"warning shot" is deadly force, a crime anywhere shooting is a crime, for good reason.
Displaying the weapon is the only "warning" allowed -- and even that is only legal if you have an Open Carry license or if you are responding to a threat.