You will have to define what you mean by "popular". Do you mean by price? Do you mean by resale value? Do you mean by actual use? Do you mean with civilians, military or police?
In the retail consumer market, the .380 that is currently selling the most often is the Ruger LCP, if that is what you mean.
It depends on the model, but most handguns will have a takedown lever or pin of some kind. Check the owner's manual for the particular model you have.
Walther, Colt, Ruger and S&W are good places to start.
Nothing. However, a Bernadelli 380 would be in the 10-200 USD range
50-175
Gun shops. That can include SOME sporting goods stores (that have a dealer's license) and SOME pawnshops (that have a dealer's license)
the 380 is a 9mm short
100-1000 depending on exactly what you have, its condition, box, accessories, papers, engraving, etc..
The value of a Titan handgun 32 cal is $159.99.
Impossible to answer without more information.
No.
NO
No.