About Engine Mount Noise--1999 Windstar 3.8

I posted a thread several days ago, to try to find out the cause of squealing noise when drive at low speed. Initially I suspected it is because of suspension. But finally I found it comes from engine mount.
When I set the gear at N, released the parking brake, and push and pull the frame, the similar squealing noise reproduces, and much louder.

In such condition, should I replace them? or apply some lubricant and watch?

And, I also wish to know what the play range of engine is of normal when push and pull.

Thanks guys.