Well, I think that animals would be unlocked asylu active certain events, or a certain amount of time has past, like in other HM games. As for animal productivity, I think that's increased by how much your animals like you, again, like in other HM games.
And I think you can get treats at either Neil's store, or Rod's
Treats of all varieties are bought from neil. Different animals are unlocked over time. You will receive a little letter in your mailbox when something changes in any of the shops (ie. new seeds, new animals, new schematics, etc.)
You will get cows, sheep, chickens and I think Llama's in your first year. Maybe not in that order. others will come later on and may require higher levels of town development. I am not 100% sure on the specifics.