Impossible to answer without knowing name of manufacturer.
Ask a gunsmith for help
No
You can get a letter from Colt. Value depends on many factors you don't address. Broad price range from 200-2000 USD.
100-500 USD or so
Between $50 of $350. Dpends on which model (there are several) and condition.
Which model?
Sorry- not enough information to answer, and no model reference as a "gentleman's pistol". To give an idea of value, we need make, model and condition.
50-800 usd
A black .38 Beretta semi-automatic pistol
100-250 or so
If you mean a Model 52, 100-1000 USD or so
A black .38 Beretta semi-automatic pistol