On mine which has a 314xxx serial (bryco arms Jennings J22). The serial number is located on the frames left hand side towards the rear. It is beneath the slide behind the safety and grip. PS: I have seen some J22's that do not have the s/n stamped in this location so yours may be different.
frame
Yes, a Jennings J22 will fire without a magazine inserted.
Probably not. IIRC, the Jennings company is out of business as a result of lawsuits. The J-22 was made from about 1981 until the company was sold a few years back, and I know of no serial number records for them.
Recommend you ask a gunsmith for help
Best to ask a gunsmith for help if you don't have a manual
.22 LR rim fire
That's a task best left to a gunsmith.
They were about $60 new, and now about $100 in good condition at a gun show.
$50 to $75. These were very crude, low cost firearms of no particularly high quality.
used about 125 (like new) - 50 (worn) dollars us. New about 150.00 Us.
Yes Provided the very cheaply made gun goes off when you pull the trigger. My advice would be to cut the gun into, throw it away and get a quality gun.