Do I HAVE to give the heart fruit to a Chao before it can start breeding? and Do I have to give it to both Chao involved?
No and no. Chao go into mating season on their own around age 2-3, and if you do want to use heart fruit, you don't have to give fruit to both chao. Keep in mind that if don't like each other, they won't mate.

~ Crazy C Lea