Logo: the value on that derringer is what you paid for it. This is a copy of a Remington (?) derringer and was made by the Italian firm of Uberti and Gardone of Italy and is fairly new. I have a Beretta pistol made by Gardone. Uberti makes replicas of western revolvers, the 1873 Colts and the 1875 Remingtons, plus others.
Your derringer is made of modern metals and should be capable of firing standard pressure 38 Special loads. I would not load anything +P into it at all.
I once had one similar to the one you show but it was made years and years ago, probably in the 1960s. It would fire on only one chamber and if you shot anything beyond a standard pressure loading the action would pop open.
Yours is probably a sturdier piece made of more modern metals and machining but if you intend to shoot it please limit your exposure to standard pressure loadings.
I do not understand what the 'HH' refers to unless it means 'Hold Here', but I sorta doubt it...
As to how many are out there - probably more than we think. Not too many folks recommend carrying a derringer as you have only two shots, not a lot of accuracy and a small grip that makes retention difficult. They are 'belly guns' in the true sense of the word, or phrase, but although not a lot of us would recommend something like that for concealed carry, it is better than a brick and there are probably lots more folk carrying one of those than we think. jmtcw.
