Cat: Make friends with Romana, and during the fall season of the second chapter, wake up after your wife. Romana will give you a cat.
Duck: Purchase a pond from Takakura and, during the summer season of chapter two, wake up after your wife.
Goat: Van sells goats when his shop is open during the spring season.
Water multiple crops
There are two ways to water multiple crops:
First is to get tartan in the second chapter and create the RC8, when the crop grow into a sprout, water it and it will water every crops around it too.
Second is easier, befriend with Romana by giving her gifts (don't give her gifts when she is sitting or she won't accept it). After you befriend her go to her room while she is in there and she will give you the Watering Can W - water 9 crops at the same time.