Is there any way to make it so that at a certain time, the player is "called" by an NPC, and can "answer" their phone and initiate a conversation with said NPC?

Sure just set a script to run after a number of seconds after doing something. With phone ringing you could show menu pick up phone or leave it, if leave have an answering machine play message or if he picks up initiate conversation.

Yeah, I have it so that an NPC calls you the first time you pick up the phone, and at other times when certain flags are set and unset.