1. It hadn't occurred to me until recently but does my telling the officer that I am armed (lawfully) give the officer the right to search my vehicle?
2. Is my telling them I'm armed give them "reasonable suspicion" or "probable cause" to search?
3. Do they have the right to enter my vehicle at that point?
4. Does the fact that I'm armed (lawfully) give LE the right to go on a fishing expedition to look for MORE weapons? I've already shown my IDs and told them where my weapon is ...
5. As seen on COPS, the statment from LE is usually something like, "for my safety and yours, I'm going to search your car to make sure ...
Keep in mind my law school memories of the criminal law and procedure issues are pretty rusty at this point, since it's not what I do, but generally knowledge of a firearm in the car gives them plenty of practical justification to search. Also, keep in mind that, in the perversity of the whole system, these "rights" will normally only be used as a justification to exclude evidence when someone who's actually guilty of something is trying to get out of it. They generally protect the guilty, not the innocent. Your assertions and questions about those rights aren't likely to stop them in that situation.
I believe the "your safety" is pretty simple, the police officer's saying that, as long as they can make sure they are secure from a weapon, they're not going to feel the need to draw a gun and shoot you to defend themselves.