Someone at the Remington Society of America web site could probably help you.
Manufactured 1919
According to the Remington website, there are three possible years for the manufacture of your Remington UMC 380, with a serial number of PA 50795. Those years are 1995, 1968, or 1923.
http://stevespages.com/ipb-remington-51.html
Condition?
Made in 1919. Check the associated link.
Depends on condition, condition, and condition. From $100 to $1,200 LNIB.
Union Metalic Cartridge Co. is a division of Remington UMC purchased Remington Arms Co in 1912 and became Remington Arms UMC.
Depends on what you mean. UMC is a brand of ammo made by Remington. UMC = Union Metallic Cartridge By Remington
fair condition 300-400.
Greatly dependent on condition. from $200 to $1,200 for new in the box.
1912
Model 51 manual located here - http://stevespages.com/pdf/remington_51.pdf