How do the sizes and shapes of the feline heterodont teeth relate to its primarily carnivorous diet?

Answer 1

Mammals display many dental patterns, as compared to reptiles, which generally have only one kind of tooth. This allows specialization in diet. Herbivores typically have just two kinds of specialized teeth: incisors, for nipping and pulling and molars, for grinding. Carnivores, since their prey is likely to resist being eaten, have enlarged cuspids or canines for killing and carnassials, also called scissor teeth, for reducing flesh to bite-sized portions. Some prehistoric cats, most notably the several species of Smilodon, had enormous canines (and adaptions for their sake, such as a wider jaw hinge and missing first molars) indicative of the very large prey they pursued.

Incidentally, cats are complete carnivores. Although Mittens may nibble on the potted plants, that's just curiousity and/or a taste for some phytochemicals, not necessary nutrition. Because they can do things such as make their own Vitamin C, felines can get all their food from meat alone.