Titanic Calico Cat

The difference between a Huge, Titanic, and Gargantuan pet is size tier, Huge is the first major tier gated behind Rebirth 2, Titanic sits above it, and Gargantuan is the largest and most valuable tier in the entire game.

Yes, you can still get event-exclusive pets after the event ends, but only through the trading market or a shop like this one, since those pets can no longer be hatched once their event closes.

Yes, Golden, Rainbow, and Shiny variants make a real difference, boosting a pet's power by 1.5x, 3x, and 5x respectively over the standard version.

No, you don't need to be at a certain Rebirth to use a Huge pet you buy, since buying one gives you the pet directly without needing to meet the Rebirth 2 hatching requirement yourself.