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?
The value of a Remington UMC .380 ACP ammunition can vary based on factors such as condition, quantity, and market demand. Typically, a box of Remington UMC .380 ammo may range from $15 to $25, but prices can fluctuate due to supply chain factors and regional availability. For a precise valuation, it's best to check local retailers or online marketplaces for current pricing.
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.
Greatly dependent on condition. from $200 to $1,200 for new in the box.
fair condition 300-400.
Depends on what you mean. UMC is a brand of ammo made by Remington. UMC = Union Metallic Cartridge By Remington
1912