I know every lvl 48 school quest pet has an interrupt. I only know that Hydra has Weakness, and Wriath has Feint I know what you're thinking "randomly cast Feint? SWEET!" So, I think that at least the other school pets have an Interrupt. Several pets, inclding the Sea Dragon, have "Spritely," which *randomly* (try 8/10) casts Sprite on the pet's owner. Also, Pet Interrupts DO NOT trigger Boss Interrupts (Cuthalla, for example, doesn't react to Pet Interrupts).
The maximum abilities that a pet can learn, at this time, is four. So a pet has the potential to have four interrupt abilities. However, this is very unlikely to occur. With multiple hatchings, you might eventually be able to obtain a pet with four interrupt abilities.
It depends on the Pet. Of Fierce Hound's 10 talents, 3 are May Cast.
You could unlock all 3 or you could unlock 0. There is also the potential that you can hatch with other pets to make it so your pet has at some point only May Cast abilities.