last question first: 6.6/88 is an old designation for the common 6,5x57
every case coming from the 8x57I case aka Model 88 was a x,x/model 88 than. notice the 7x57 is not a M 88 but a Model 93 because th 7x57 developt for the spanisch model 93 was a case by its own.

most dont know that the 7x57 case have a bigger base than the 8x57.

in 1911 Dreyse became Rheinmetall Sömmerda or RMS but "Dreyse" was still used as brand. I dont think that RMS was the maker of this little Mauser or "Mauserlein" but see some smaller firm in Suhl- Zella-Mehlis as the maker. have never seen this rifle before but it would be a a nice small bore rifle, no doubt.
RMS "Dreyse" made in this times only the Model 1907 Pistol and the semi auto carbine