Should MUST always follow HAVE .Eg That MUST HAVE been really difficult for you.

since That is a singular why can't we use HAS in place of HAVE? 

I found something about MODALS in my google search but I didn't understand it.Please explain.

And one more doubt..

What is the difference between Doesn't and Don't..

Eg: He doesn't want to be killed..  but why doesn't ? why not don't...