I've been sending letters to Sara hoping that she would reply back to me telling that her freakin' pendant is broken.However,she has not replied to any of my letters.So I wonder.....do I need wi-fi to receive letters to the NPCs?

Yes. You need to exchange about 7 letters with another person, or people. Actually, you can just use wireless DS communication, iirc. So, if you've got a friend with a DS and III, just send each other letters.

Once you've exchanged that many, you should be able to get the 4 letters (per NPC) you need to start the various side quests.