OK, maybe you have less research on them than I thought. I am not a collector or antique arms expert, but I do have a copy of Flayderman's Guide to Antique American Firearms. In order, I see:
Colt 1849 Pocket Revolver .31 cal., 325,000 made 1850-1875 plus some in London, which would be shown in the barrel markings.
Pocket pistol. If marked Deringer Philadela it is the real thing made by Henry Deringer from the late 1830s - 1868.
Model 1816 Flintlock Pistol .54 cal., 19,374 made 1817-1829 by Simeon North for US Army issue.
Remington New Model Pocket Revolver .31 cal., 25,000 made 1863-1873
Rogers & Spencer Army Model Revolver .44 cal., 5800 made 1863-1865. If it does not have "RPB" inspector's mark here and there it may be the much less common civilian model.
Model 1855 Percussion Pistol - Carbine .58 cal (for the Minie ball as used in rifle muskets of the period) with Maynard tape primer; 4021 made 1855-1857. Look through Dad's effects for the attachable shoulder stock to bring it into carbine configuration. That would add a good deal of value and interest.
Model 1842 Percussion Navy Pistol (Sometimes called 1843) (The Army model had an outside hammer, the Navy has the "boxlock" you show.) .54 cal., 1200 made by Henry Deringer, less than 200 rifled like yours. Another 2000 from Ames, all smoothbore.
I don't know about appraisals. I figure they are good for insurance policies and bragging rights. Real value is a cash offer to buy. You can look for asking prices at Gunsamerica.com and completed auctions at Gunbroker.com and Auctionarms.com There may be some real antique firearms sales sites I am not aware of, maybe somebody will post them.
For example, there is a Rogers & Spencer awaiting a $1650 opening bid at Auctionarms and an 1816 North flintlock with an asking price of $2500 on Gunsamerica.
