On a 124 the two tubular mounts are used to secure the differential's rear cover to the rear subframe, there is a tool to extract old and install new ones, this can also be accomplished with a large bolt/nut/washer/very large socket set up as a puller. The other style mount is essentially two rubber washers and two cupped steel washers is used to secure the differential's front mountint point. This front mount uses an 8 mm Allen cap screw/bolt from below up thru the washers and then screws into a 17 mm nut which rests inside a channel formed by the rear subframe structure. This 17 mm nut can be somewhat difficult to secure when unscrewing the bolt, I've usually been able to get a 17 mm wobble socket on it when used with a T-bar.

The only other issue will be the ABS sensor located in the differential housing, this can sometimes be difficult to remove. First the 5 mm Allen screw needs to be removed, the usual care to avoid stripping it is recommended. Once the Allen screw is removed you can use a hammer and drift to gently rotate the flat steel plate part of the sensor to loosen it. Then you can again gently pry the sensor outwards from its hole in the differential case, this can sometimes be quite difficult as the sensor is a tight fit and it has an O-ring also. You should order a new O-ring as the original will likely not fit back into place correctly and will leak. The o-ring is of very thin profile and will not usually be found or available in/from the standard style assortments of rings and a thicker one will not allow the sensor to seat all the way or to seal up properly.

Depending on the car and the rust situation underneath an alternative course of action is to lift the rear seat back and disconnect the sensor plug in the cabin, push the grommet and plug out under the car, remove the 10 mm screw holding the sensor cable bracket to the subframe. Then remove the differential with the sensor in place. Then you can deal with the sensor with the differential on the bench. Good luck!

While you're up underneath there its a good time to inspect and/or replace the flexible fuel hoses coming to and from the tank and its vent.