Q:

Can settlers wear power armor?

I am building a settlement and I want to know if settlers can wear power armor. If so, can they take the power armor if the power armor is on display on a power armor rack?

A:

Yes. They tend to do it without your consent if you happen to leave fusion cores in your power armor. If you've never had this happen, you are unbelievably lucky.
To answer your question: "Can they take the power armor if they are on the power armor racks/stands?"
Based on this thread:

As topic says, we were invaded and a settler stole my suit of power armor off the rack it was on

Based on later posts by OP, he had left a fusion core in the suit:

the settler left the suit there with about 5 charge left in the core

So, as implied earlier, unless you want to lose your power armor with no warning, take the fusion cores out of your power armor.

