Should the whole strut assembly move while the car is jacked up?

[Eg.h2o]

The floating suspension does NOT create vibration in the steering wheel if everything is in spec.

[Racoon]

The floating suspension does NOT create vibration in the steering wheel if everything is in spec.

how to prove that everything is in spec?

[Eg.h2o]

The first thing you will notice when the mounts fail will be the clunking noise. If you drive it that way for a LONG period of time after that you may notice the car pulling in one or both directions because the mounts are too loose. Then WAY longer after that you could notice the steering wheel jiggling and vibrating as you drive down the road.
as far as making sure everything is in spec I would take the car to be inspected at a garage you trust.