I found out that some are for my avatar, and some are for my pet. If I use them on my pet, what happens?

Do they have a "Play with pet name" option on them? Some items from the Grooming Parlour count as toys, so they can be used to play with your pet. These will just make them happy, unless they are already at full happiness.

Ahh, I see. How do I change my pet's image? Like, my pet is just a fish atm lols

That depends on what you want to change your pet into. I suggest looking at species and colours to see what you like the look of, and then look up how to get that pet. There are also Experiments.