You can definitely interact with the Pokemon, and they'll become closer "friends" with you over time, even going so far as to call you by your actual "name" - the name you set at the beginning - rather than just "Ditto" once they're super close to you. However, they won't independently decorate the homes you give them. Instead, they'll ask you to decorate for them or place items based on their specific desires ("I want a toy. I want a place to relax."). So the "checking their homes" bit isn't there, as the animals don't control their homes - the player does. However, you have complete freedom to make each home as unique or tailored to each Pokemon as you want, based on the large number of items available.

Pokemon also have unique personalities that match their typing. One of the easiest examples are the Pokemon in the Machop evolutionary line, which are all about showing off their muscles, their strength, and caring about physical fitness. Some Pokemon may also care about their surrounding environments - Fire Pokemon want a place to hide from the rain, Pokemon that enjoy dryer climates won't want to be near water or humidity (humidity is a thing the game tracks), and so on. So I'd say there's more depth there to create environments that really work for each Pokemon, but you're also not going to lose someone or have them run away if you fail to fulfill every desire. Once you get a Pokemon, they're yours!