The CROWN – crownN proofmarks with the gauge number 248, butwithout date or ledger number show the rifle was proofed by the Suhl proofhouse before 1912, using the "4000 atm Special Proof Powder". The gauge number 248 stands for a bore/land (not groove/bullet) diameter from 6.75 to 6.99 mm = .266" - .275". This, combined with the time span and the service load marking 2.5 g = 38.6 gr Gewehr – Blättchen- Pulver = (military) rifle flake powder , points to the 7x57 aka 7mm Mauser aka 275 Rigby. Suhl made barrels then were often bored quite tight, sometimes even below the later, 1929 on, minimum standards.
I can not positively identify F.A.K., as there are too many possibilities. It may stand for F.A.Klett, a barrelmaker, or Fritz Albert Kessler, or someone else then activein Suhl.
To further identify the Mauser action, M93 – M96, please post another right side photo of the action with the bolt open.
The scope mount bases are for the claw mount variation once made by Albert Wilhelm Triebel, Suhl.