"Mag er mich?" is translated as " Does he like me?" My question is does "Mögen" is used also for probability... so my sentence about it I am confused "May she missunderstand me by that? " is translated into German as "Mag sie mich damit missverstehen?"
You're right in that
mögen may be a modal that used to be used like the English
may in the sense of probability and a full verb equivalent to the English
like. Nowadays, the modal
mögen is rarely used generically but mostly in fixed phrases like
Das mag so sein, aber ….
So your translation is correct but would probably be understood by many people as Does she like to misunderstand me?. Unambigous translation would be
Wird sie mich damit missverstehen?
Könnte sie mich damit missverstehen?
depending on the level of probability you're asking for.
Yes, it is. Another example is:
Look at Bedeutung number 1.a in the Duden.