Yeah, I got one in T16 this season too.
There’s a specific corner room it spawns in. It’s in Cathedral 1. It’s a square room off of an L-shaped corner tile, with an entrance from either side of the L. It looks like this (image not mine, courtesy of IcyVeins):
It always spawns in that orientation, too, you won’t see it spawned in a different rotation. So depending on where you start from you can either run down (if you start near the top) or to the left until you get to the area in the bottom left corner of the map, and the room should spawn near there.
This IcyVeins guide might be helpful for your hunt: How to Access Whimsyshire and Craft Staff of Herding Guide - Diablo 3 - Icy Veins
It tells you where to find each item, and has some helpful pictures of the locations so you know where to look.
They are different pets. You right-click on them (I think? I’ve had them all for a while so it’s been a while since I had a new one) to “learn” them. Then in your Cosmetics menu (accessed by F1 unless you’ve changed the default keybindings) you can choose one to equip. They follow you around and pick up gold for you. Don’t get rid of them, you might as well “learn” them even if you it’s one you don’t like and won’t use. No harm in having them available in your cosmetics menu.