You don't need to remove the strut to remove the strut mount.

Raise the car - put the body on sturdy mounts.
Remove the wheel, put your hydraulic jack under the control arm so it doesn't move downwards.
Undo the nut on top of the strut. you will need a 22mm ring spanner + a either 7mm or 8mm allan key (depending on whose strut is installed).

Pull the strut piston down from the strut mount (do this in the wheel arch).
You need to loosen the rubber cover.
The strut mount has three bolts holding it in and will need to be removed via the wheel arch.
If the strut piston is easy to compress then the strut is cactus. If there is a leak from the top of the strut the strut is cactus.
The bump stop will be probably cactus. You should get a new one with the strut mount kit.
Replace everything in order of removal.

Doing the bounce test on a W124 will not give an indication of the condition of the strut. To ascertain the condition, MB workshops should remove the strut and measure its compression on a tester.

A strut should give considerable pressure when trying to compress the piston. If its soft - it's had it. In my experience if the strut mounts are split then generally the strut is stuffed also.
If your car has 100,000 K's up the struts will be at the end of their life.