With the extra pics, I see a couple of more things.
I think I see the rifles ser# as 5583 on the LH side of the recv'r.
I see 5583 on the bbl LH side as well but can't make out what 2 digits/letters are after that.
Matching numbers on bolt body and the bolt parts I can see.
(The bottom metal (the trigger guard magazine box) should be #'d the same on the outside back wall of the mag box. You have to take the bbl'd action out of the wood to see it of course.
Mauser Sporting rifles were ser#'d in their own series separate from the military production.
Starting w/ #1 in 1898.
A four digit ser# in the 5000 range would be a in the 1902/early 1903 production time.
So that seems to match up with what info I have.
The roll die impression on the recv'r ring is consistent with with production up to 1922. The Mauser name was changed that yr to Mauser-Werke, AG. from the previous used WaffenFabrik Mauser, AG.
The latter marking is on the OP's rifle along with the yr/mfg/proofing which would be correct.
The commonly seen Mauser 'Banner' marking wasn't used til 1909. But it wasn't used on Mauser rifles till after WW1, around 1924/25.
It was used pre-WW1 on pocket pistols and a few other offerings.
The front sight is called a 'Block Sight' and was one of the 3 types avail on the sporter(s).
The base 'block' is soft soldered to the bbl and dovetailed for the sight insert.
Some bases were slotted for a sight hood.
Rear sight 2 leaf blade was an available option as well at the time.
A block base soldered to either the bbl right in front of the chamber profile. Or onto a sleeve extension placed on the bbl to lengthen the look of the chamber profile and act as a riser for the rear sight.
DST was a common option chosen. Though plain Military pull single trigger and a Single Set trigger were also avail.
Most of the parts to these will be ser#'d with the last 2 digits of the rifles number.
The Bottom metal with it's floor plate release inside the guard is one of the 3 option types.
One was a plain military style where you need a pointed instrument (loaded rd) to push in and release the plate.
The other was the well liked by collectors lever release on the floor plate.
Normally there should not be any small Lock Screws in the trigger guard to lock the action screws in place as on a Military rifle. I believe that feature could be ordered, but not completely sure.
Check the magazine ser# for a match to the rifle and it will tell you if it's orig or not.
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It looks like it has the Pear Shaped bolt knob and that was pretty much the standard on sporters, though again,,order what you like.
The shape is called an Oberndorf style bolt knob oddly enough.
Caliber, if not imprinted on the bbl LH side at the breech along with the ser#, should be on the bottom of the bbl up near the breech.
It will be in BORE dia M/M's, not groove dia.
Case length usually along with it. Sometimes rifling twist in 1 turn in so many M/M's.
Early guns like this can sometimes have bore dia expressed in a gauge size and caliber in a number system God only knows how it works. But there are websites like the German Gun Collectors Assn that explain and have charts.
Mauser had their own Gov't sanctioned Proof facility in Oberndorf right across the river from the main factory.
Those added NAZI era proof marks (Eagle/N, Eagle/J) on the bolt handle (1937? to 1945) are one thing that is newer than the rest of the rifle that I can see,
The rounded grip knob of the stock was the standard style early on.
I think I have the following in the right order..,,forgive me if I'm wrong....
If the forend tip has a Horn or Ebony Schnable shaped tip attached, it;s a Mauser Type A sporter
A Schnable forend tip shaped of the stock wood itself, It's a Mauser Type B Sporter.
I reload and shoot a couple .318 'J' bore 8X57's
I load either cast or jacketed bullets intended for the 32Winchester Spcl. These are sized .320/.321.
I load very conservatibly for the rifles and have had no issues. Starting loads in the manual for 8x57 are my primary loads.
I use regular 8x57 'S' bore dies (common) but remove the .323 expander button from the decaper rod and sub a smaller caliber button to hold the decap pin in place. So it just decaps and does not expand..
The idea is to not open the neck back up on the return stroke of the press. The sized but not expanded neck of the operation provides a perfect seating tension for the smaller .318/.320 dia bullets.