Hi Steve, welcome to the Luger Forum. It sounds to me like you have a standard byf 41, with a substituted side (trigger) plate. The script "r" is part of the serial number (4558r). Your pistol was completed about April 1941. The byf is a German Ordnance Code and signifies the manufacturer (Mauser). The 8,82 is the diameter of the bore, across the lands, in millimeters. Most European countries use the comma, instead of the decimal point, so in the US it would be 8.82.
The right side receiver marks are two eagle-over-655 and one eagle-over-swastika. The first two are German Inspection Office (Waffenamt) marks and signify compliance to specifications. The third mark is a firing proof mark, which indicated the pistol was successfully fired with an over-pressure cartridge.
With the mismatched trigger plate, your pistol would be classified as a "shooter", rather than a collectable. So go have some fun with it!!
Hope this helps!