The crown/n indicates this gun was made for the commercial market and most were made in the 1920's pre WW2 Weir-mar era.
You have given us lots of nice pics but sadly the more important areas you have not shown us.
Specifically the underside of the gun where the barrel meets the receiver.
Attachment 85882
If you see an 8.8# (ie: 8.82 - 8.88) then you have a 9mm barrel.
If you see a 7.65 then you have a 30 cal barrel or 7.65mm
On very early Lugers like the 1900 above it gets crazy.
If you find a 172,28 that is the amount of lead balls, the same size as the bore, it takes to equal one pound (Europeans use commas not decimals) then you have a 30 cal barrel or 7.65mm. This is the old European method of measuring the bore. The Luger would also be 'BUG' proofed as seen above.
Clear as mud ??
I thought so.
At any rate I love your Luger even if it is a Heinz 57 mismatched, refinished, over polished example ... it has a certain charm only shooter grade guns achieve but that's not a bad thing. Enjoy it, learn from it but most importantly have fun ya ??