The dimensions I show for the 6.5X52R in my DEVA manual indicate a rim diameter of 12.60mm and a rim thickness of 1.6mm. The same text gives the rim diameter for the .30-30 as 12.85mm, while specifying the same rim thickness. That translates to about .010" difference in rim diameter.

You might want to measure the rims of the cartridges you are using against these standards.

The other possibility is that the rifle is chambered for the .25 Remington, an obsolete cartridge which is the rimless version of the .25-35. Since the rifle is marked 6.5X52 without the "R", I would think this was a possibility. The .25 Remington has a rim diameter of .421, the same as that of the .30 Remington, a rimless version of the .30-30, but the shoulder is somewhat farther forward than that of the .25-35, so that a .25-35 cartridge would fit in a .25 Remington chamber, but not vice-versa.

How are you trying to insert the cartridges into the magazine? The only picture I could find of a Zi-Di rifle and magazine showed the magazine to be similar to that of a Model 43 Winchester .22 Hornet or .218 Bee. It appears that you would start with the cartridge rim half way toward the front of the magazine and push the follower down with the cartridge, while at the same time pushing the cartridge toward the rear of the magazine and under the magazine lips.