amixam 1992

I could not find an answer. Is it essential to replace the strut mounts when replacing the struts? Mine is a 1992 SE 5 speed, no Sonor. I understand that the bellows need to be new, but how long are the top pieces supposed to last? What should I look for when replacing the struts as far as wear on these?
Note, I have had the car for two weeks, and am not yet steeped in the knowledge of this car. I appreciate this forum, and hope to have an answer soon. I also suspect the trailing arms need to be gone through on the rear, as well as most any suspension rubber piece.
The car will not stop bouncing. The rear struts are non existent.
It will shimmy from side to side over bumps and causes an uneasy feeling. I planned on being able to move my children in it, but frankly, I'm too unsure about the car being safe to do so. By the way, the car has 207,000 on the odometer.
Any input appreciated.