My best guess it either an 1893 or 1895 Mauser. If you remove the bolt and look at the bolt face, if the bottom of the face is square, it's an 1893. If it's round an 1895. There are some called 1916's IIRC, and they're, again IIRC just a later 1893, possibly with slightly better materials. The hole in the receiver ring throws me a bit but possible that was done later by a gunsmith to help with escaping gas problems inherent in those models.
There is some controversy considering the stength, or lack of strength in those rifles. I'm not sure as I've seen some converted to 7.62 NATO that were imported by Kimber, sporterized and sold as .308's. Supposedly they were checked and pronounced safe.
If it's still a 7x57 Mauser, that's a decent hunting round as is. Finding ammo can be a bit sticky but most large LGS have at least Federal 140 and 175 gr. ammo and it's fairly good stuff. My preference is for the Winchester 145 gr, Power point in factory but it's hard to find and only made seasonally.
On reloading, if you do reload, most manuals state to use only the starting load. There's an article in the November Shooting Times by Allen Jones who used to be the ballistician who did the load work ups for many of the Speer manuals. he stated that one could work up to the middle loads shown in most manuals and still be within the safe pressure limits for those rifles. I would have no problem using a Federal 140 gr. factory load in that rifle for deer, even out here in the west.
I wonder if there are any markings left on that rifle. Would help in identifying it better.
Paul B.