Does he have the right to take this person's hearsay and automatically turn it into truth? Yes. While that is seldom an advisable thing to do, he may do so if he wishes.
Shouldn't he have coached me previously if there were supposed issues concerning my conduct at work? Generally, yes, that is the accepted and proper way to do things but he isn't required to.
I have always done what was asked of me and at the beginning of my employment my manager said that he had plans for me to move up into a higher position. Do I have the right to take any legal action? Since your manager hasn't done anything illegal, there is no legal action to take.
Was this a wrongful termination? No. Not even close.
If not why? Because there are no laws that prohibit your manager from terminating you for this reason.
This termination totally took me and other workers by suprise. My district manager said he felt awful about what happened and was going to look into it. Then perhaps he will reverse the decision but that will be entirely his call. The decision to fire you may have been very unfair but it was not illegal.
A person, who is nice to you, but rude to a waiter, is not a nice person. (This is very important. Pay attention. It never fails.)