Can't be done without a detailed description of all features and overall condition at a minimum
What is the value of 1903 colt pocket pistol.32 calibre?
The .31 caliber pocket pistol is based on the volcanic repeating arms company's .31 caliber lever action pistol using rocket ball ammunition( I think, but don't rely on my answer if your question is for something important because I might be wrong.)
Old catalogs
You need the services of a professional firearms appraiser
Lots of makers made 25 cal pocket pistols. Embellishment may or may not be done by the maker
impossible to answer without a detailed description of all markings.
How much can you sell a car for? Depends on the car. Your answer depends on the pistol. There are inexpensive 22 caliber "pocket" pistols that sell for about $50-75, and VERY pricey .22 caliber Olympic competition pistols that are $1000- and up.
if it's a 380 caliber then made about 1924
Value will depend on exact configuration, overall condition, finish, box, manual, accessories, serial number, barrel length, etc.. Range could be from 25 USD to multiple thousands of USD.
A .44 caliber derringer.A small pistol called a Philadelphia Derringer.
10-50 USD or so
You can call Colt and give them the serial number or you can look it up in the Blue Book of Gun Values.