Sounds like you have a Browning 1910 pocket auto (Browning has made a couple of different .380 autopistols over the decades).
If yours has the tall adjustable sights and a finger extension on the magazine, it is technically a model 1910/71.
The basic M1910 was made in .380 or .32 ACP caliber, and could be changed to the other caliber by swapping the barrel.
#1 -- Don't know.
#2 -- Here are a few links to auctions or online For Sale ads to give you an idea what other folks are asking for their pistols. Remember, condition is VERY important in setting price; a few small scratches, a worn finish, cracked grips, etc. can reduce the value quite a bit.
Item:9559862 Browning Arms Co. Browning .380 auto, made in Belgium For Sale at GunAuction.com
ARMSLIST - For Sale: browning 380
ARMSLIST - For Sale/Trade: BROWNING 10/71 .380 AND WINCHESTER 94 30/30
#3 -- I'm not seeing a manual at any of my usual sources, but here is an article about the gun which may answer some questions about it.
1910 FN Browning
#4 -- In addition to the article above that has a brief explanation of disassembly, here is a YouTube video clip of disassembly of the Browning 1910.
BROWNING FN 1910 field strip - YouTube
"Placement is power" -- seen in an article by Stephen A. Camp
(RIP, Mr. Camp; you will be remembered, and missed)