IN reply to your enquiry about the cartridge cases, they are most probably 7,62x54R (Imperial Russian) cases,used from Late WW I to the 1930s;
The Ottoman Empire, during WW I, received thousands of Mosin Nagant M1891 7,62 Rifles from Germany, which had captured them from the Russians at various Battles in 1914-15. They also received Millions of rounds of captured ammunition (Brass cased). After WWI, with the formation of the Turkiye Cumhuryeti, in 1922, Ataturk negotiated with Lenin of the new Bolshevik gov’t of Russia, to settle the Armenian Border question with Turkey. As part of the deal, The Turkish Army received a large number of Russian M1891 Rifles.
Turkey used these Russian rifles (from Germany and Russia) till the early 1930s, and disposed of many of them to the Kingdom of Afghanistan, amongst other Islamic states in the 1920s as part of Ataturk’s Policy of helping middle eastern nations to achieve independence from foreign Pressures and influence.
Others of these rifles were exchanged with Finland for Mauser rifles and Timber and Paper Products and other goods.
I would advise you to go to Gunboards.com, a forum which has a lot of information about Turkish rifle History,
and also Parallax’s Curio & Relic board, which has my analysis of Turkish serial Numbers 1929-1955 of all the rifles made, converted, assembled by the Askeri Fabrikalar organisation of Ankara and its various sub factories; ( Doc AV Turkish Serial Survey); there are other texts there with further history.
The questions raised by your find give us a lot of detail of History (Political, Military and Industrial) about the WW I-Republic period to explain in a simple Post. I have a large collection of Turkish Mauser and other rifles, from a M67/12 Peabody, a M1887 Mauser through to an ATF 1954 refurbished WW I German Mauser (Askeri Tufecki Fabrika)
I also have a couple of German marked, Turkish re-marked MN 91 rifles (“Kal 7,6”) in Turkish script ( Pre-1929 change to Roman Letters.)
There are several very good Biographies of Mustapha Kemal “Ataturk”, which give a lot of detail about his involvement with organising both the Turkish Army and in the early 1920s, ASFA, as well as his Foreign Policy aims and assistance to middle eastern countries, as well as Trade relations with Europe’s “NEW Republics” (Finland, Poland, Czechoslovakia, etc.;).