2 - Yes, you can refuse. Be aware that there are some significant negative results to be expected from doing so.
2a - You may want to assess the level of paranoia you seem to have regarding imitation cops.
3 - Why are you "willing to be disarmed by a real officer for his or her pace of mind" if you have done nothing to demonstrate or suggest that you have any ill intent? Same question regarding "for my own safety and peace of mind"?
The administrative manipulation of a firearm only increases the chance that it will be mishandled, resulting in a negligent discharge which may result in physical injury. Is not the LEO as safe if you just don't touch your handgun?
How do you feel about the "habit" of some LEOs applying handcuffs during even a consensual stop "for officer safety"?
Given your admitted paranoia that the person in front of you may be an imitation LEO, how/why is "[your] own safety and peace of mind" enhanced by surrendering your weapon?
Presuming the encounter to be, at least in the beginning, a consensual stop, why are you willing to accept a violation of your 4th Amendment rights in order to facilitate the "safety and peace of mind" of the LEO and yourself? (Are there other rights you are willing to allow to be violated for the sake of "safety and peace of mind"?)
BTW - I am not known as one who climbs on soapboxes and shouts that all violations of constitutional rights must be forcefully resisted on the spot where/when any violation occurs. There have been numerous discussions of how to indicate your disagreement with the violation of your rights that does not put you in high jeopardy of getting beaten/shot right then and right there. While the search function here is wonky, and the advanced search often just as wonky, I suggest you try to find and follow at least some of those discussions. And while you are at it, do a search for "digital voice recorder".
In closing, we are quite a bit leery of folks who say "I am a supporter of __ but ...." I don't know enough about you yet to suggest that you fall in that category or are an over-zealous Constitutional Rights warrior, or somewhere in between. Stick around and let us get to know you.