That is a CZ-27, a somewhat simplified modification of the .380 caliber CZ-24. The CZ-27 was made in large numbers for the German forces after Germany took over Czechoslovakia, because 7.65 Browning (.32 ACP) was in the German military supply system while 9mm Short (.380 ACP) was not. There were a couple of marking variations but the total production was around 476,000, 215,000 being of that variation. They were widely issued in the German service and were probably the most common European "bringback" pistols next to P.38's and Lugers.
Gun Parts Corp (
www.gunpartscorp.com) has after market magazines.
I see nothing that would indicate the gun is not perfectly OK to fire.
Since you have the sideplate off, lubricate the works with a few drops of gun oil, and wipe it down with oil or something like G96 Gun Treatment to kill any rust. The only part that sometimes breaks, aside from the front bottom of the grips, is the tip of the safety release (the part with the button in front of the grip). The gun is quite easy to field strip, but I don't recommend going beyond that unless you have some experience.
As to a reblue, that is up to you. It will not really increase or decrease the value, since the guns are so common that there is little collector value. Current sale prices for that variation in that condition would be around $200+.
HTH
Jim