Yea. In order to recruit her you need Magic 6 to reverse her suggestion spell and a high charisma (like 8-9?). I believe that's how you get her to follow. It's been awhile since I've done it.
And yes each area has some unique characters to meet and again there are some "hidden" ones that require certain things to happen. Another example of a hidden one is Lupa. She's unlocked after helping the brothel madam with all of her quests.
The Bunny character is only randomly encountered when you're indebted to the bank in the first town and have your debt increase a few times.