So, it's very likely someone was messing with the trigger, plate and possibly the trigger linkage.
You'll need to check and verify it is correct prior to firing it. Start with one cartridge at a time, then move to two. I don't generally put more than 5 in a Luger magazine.
I don't have any EG or replacement trigger plates to compare this one to. If there is no number inside the plate relating to the first digits of the gun's sn it is a likely replacement. In any case, the plate looks like a replacement.
Here, for reference, is the side plate and trigger area from my 1938 Mauser Luger:
You will notice the shape of the plate, the corners and the shape of the part that encloses the trigger transfer bar.
Nothing you can do will "restore the gun to original condition" and regardless of finish replacement it should never be represented as "original".
The star in that location inside the receiver or frame is typically an internal factory inspection mark done by a Mauser worker as the part moved through the manufacturing process. That shaped star was also used as an acceptance mark by the French occupants of the Mauser factory after the war.
The finish has a dull appearance and may be a dip refinish.
Assuming the trigger linkage is correct, reliable and working properly, you have a nice gun for shooting.
Don't be anxious. The price you paid is appropriate for that.