I believe it should be written as "...to meet you" rather than "...to meeting you"; just as one would say: "I look forward to hear from you, soon" rather than "I look forward to hearing from you, soon".
A. The employer is right on this. It should be, "I look forward to meeting you" and "I look forward to hearing from you."
"To" in these sentences is a preposition. The object of the preposition must be a noun or a noun substitute. "Meeting" is a present participle, which can function as a noun subsitute. "Meet" is a verb and cannot function as an object of a prepositon.