When it comes to how a mechanical device should feel it hards to describe, I would try to find another car like yours at a dealer lot and compare. But the real test is while driving through a turn on the road or in a parking lot see how accurate you can make corrections at the same angle as when stationary-and you get the play when stationary, if the helm follows your commands while moving then the front suspension is probably fine. But my car a 1998 c230 does have tons of play and assistance when stationary and turned, it has to do with designing a front that is easy to maneuver when parking. And the play when steering is straight is a good test for a front within spec, but is a totally different item from a turned wheel.

Wandering can be alignment and rear alignment, I've heard different stories about adjusting rear suspension on the C-class so you may also want to shoot some digital pictures of the rear diff mounting and compare with another C and see if things have collapsed. Tires whether worn or a tire design that dosen't compliment a rear drive or C-class can be an issue. And make sure no heat shields under the car have dropped and are catching the cross winds.