What is heritage?  some of my pets have 3 green stars and one of them has 3 pink ones and green ones. I was wondering what that means? does it affect anything?

Green stars mean your pet has the Descendant of Heroes moniker. Each star increases your pet's stats across the board.

To get stars, you need to level both parents to level 50.

Red stars are degeneration grades. It means the parents are related within three generations.

Red stars give bad genes, so they do affect the pet negatively.