Are the collisions between the real gas particles perfectly elastic?
Well, what is an inelastic collision, really? Suppose you have two balls made of steel; they collide, then fly away with some lasting deformation, so some energy is lost. With molecules, it is not quite like that. You can't leave a dent on a molecule. It has certain discrete energy levels, and that's it. You either excite the molecule to one of these levels, or you don't excite it at all.

To sum it up, some collisions of molecules are perfectly elastic, and others are combined with excitation of some rotational or (more probable at higher temperatures) vibrational mode in one of the molecules, or maybe in both.

Noble gases which have no molecules and hence neither rotational nor vibrational modes may enjoy perfectly elastic collisions up to pretty high temperatures.