First question is, is it normal to replace strut mounts when installing new struts?

If I can twist the top portion of my struts, under the hood, and it moves freely, is this a bad strut mount?

Are squeeking noises going over bumps a sign of bad strut mounts? I have replaced the struts, new sway bars, ball joints, control arms etc....

What are the long term effects of a bad strut mount?