Well I see the slide is serial numbered, so. It also IMO could be a police issued gun, with either Eagle/C, Eagle/F, Eagle/K or Eagle/L marking. That marking would probably be on the right. Often when the slide is serial numbered, the gun was issued somewhere to someone.
In those cases above, it would IMO be worth a premium over say a nazi commercial "shooter". Also, refinishing it is not worth doing UNLESS you can definitely make it look better than what it is IE a more original look to the finish. If you refinish it a second time improperly, it will be a waste of time, money and efforts.
It is listed on both the slide and the frame. Everything matches but on the slide the third digit, the 1, has been stamped over a zero.
That could be. If so, it was probably done shortly after production. Maybe a factory error? At the end of war, many PPs were factory mismatched because they did not have the time to pay attention to such details. The SN you gave is 1944 production based on a chart on the PP & PPK forum.
You can take surprisingly nice pictures with a basic digital camera by using a fairly bright (but not really bright!) indoor location, mounting the camera on a tripod or at least some sort of improvised solid rest, manually turning the flash OFF, and shooting the picture using the timer feature. You don't need to use the 10sec timer like you would for a self-posed portrait; this is what the 2-3sec timer setting is for.
Unless the camera is really cheap, turning the flash off in indoor light will cause the camera to self-adjust and lengthen its exposure time. It's essential to use a tripod or rest because most people physically can't hold a camera still enough to prevent blurring during the long exposure.
I prefer taking them outside on a neutral background. I also try to photograph guns at a slight angle to eliminate glare. The other trick is to wipe the gun down with oil to eliminate any smears or fingerprints. I also leave my macro setting on for the most part. Make sure you get the "green" go lines before you shoot the pic, because "red" means the camera expects a pic in that moment to be crappy.
Here is an example of my Walther and my way of photography:
Walther PP, 1941, E/WaA359 accepted. Its a high polish gun, which only approx the first 15k were. After those, these PPs such as yours had a dull military blue which was more efficient for production. It also has a SN matching mag which is thought to represent Luftwaffe contract.