Considering the general layout of the stock, grip and receiver, I'd like to believe this is based on the H&K MG5, but obviously built upon to hearken back to the MG42 Sun's mom uses.
Considering the MG42 was only used briefly considering the history of warfare (it only saw major use during WWII, and then afterwards was succeeded by later designs), I think it'd make sense for Hina to be the only one with it in the family. I mean, Luna uses an AR-15, and AR-15 receiver guns are everywhere. I think it's good that Hina still has it.