I've always used pumpgun mags in my autoloaders because the bolt will close on the last shot allowing for quicker reloading.
The actions on these rifles are of a uniform length, so the clips for one calibre will fit in a rifle chambered for another, however, I'd be hesitant to try to use clips for cartridges of different lengths. The same clip for a .270 will work with a .280, 30-06 and .35 Whelen and vica versa, and likewise a .308 clip can work in a .243 rifle, but when the cartridge is shorter, Remington puts a spacer in the back of the mag. Using a 30-06 clip in a .308 would allow the bullets to slide forward and back (with recoil) leading to jamming.