By law, can people be mandated to wear masks in public?

Yes, unless and until the Supreme Court says no.

It differs by country. But in the United States, yes they can if it's during a National Emergency (which has been declared).

In my country it is mandated (by government).

A law can tell people to do anything. Whether it's reasonable is another question.

Well I'm sure you'll have retard Karens shaming people in public, you may have Karens who won't let you in their stores without a mask, then you have the low iq cop who arrests you. It's definetly possible

That's a good question.  Local municipalities require us to wear shoes and a shirt when going in to a grocery store or restaurant.  The face mask could fall under those types of requirements.   
Out on the street?  I guess if you're required to wear pants - the mask isn't much of a stretch.  I would expect this to get tested in court.