Could вас be used in place of вам?
Call = викликати - вас (genitive)
Call = дзвонити - вам (dative, think of "to give a call")
Is there are difference between the two meanings?
дзвонити comes from дзвін (ringing). It means "to ring", in both meanings: to ring a bell (in its literal meaning) and to make a telephone call.
викликати - to demand or ask for the presence of, to cause, to challenge
You could say "Я не буду дзвонити до вас." if you really wanted to use вас
Can be won't?
How do you say: Don't call me, I'll call you?
And does it have the same meaning?