Is what the questioner did, regarding her previous conversations with her relative, and what she is thinking of doing, in terms of spaced out and reserved conversations, considered Haram? And is it permissible for her to speak with him infrequently and about superficial topics with the intention of future marriage?

You must repent from conversing with a non-mahram (definition) man, for companionship is not a true necessity that permits it. This door is dangerous and a means to corruption. You both should hasten to marry when possible, and studies should not be an impediment to it. If marriage is facilitated, then that is excellent; otherwise, each of you should separate from the other.