No, Diseased Mechafish doesn't do anything to your pet. I think that was also answered in a NT Editorial recently.
Color:
Glowing Jelly can turn your pet Glowing.
Chocolate, Garlic, and maybe Coconut foods can turn Chias/JubJubs/Kikos into those colors.
There is an RE that turns your pet Invisible.
Gender:
Cape of the Sun will change your pet from male to female (not the other way) if you use it in the BD.
Species:
Don't forget the Magical Toys.
Abilities:
You forgot the obvious Bottled Faeries
One of the wheels has a raise ability level result on it.
Health:
Worm items cure Pteris.
Cheese items make Skeiths sick.
Ice Cream items make Quiggles sick.
Apple items make Kyriis sick.
The Wheel of Misfortune has a result that will give a random disease.
There are quite a few weapons that give diseases. Look for Darts and items with Poison in the name for some examples.
Glowing Jellies can give Blurry Vision.
All of the Desert Scrolls about curses can 'backfire' and give some (random?) disease
Mood:
I think losing hitpoints from the wheels can cause mood to go down.
Hunger:
Eating a Turkey Dinner will make your pet Very Bloated, regardless of hunger level.
Reading a Scroll of Hunger will make your pet hungry (not sure how much).
Dining at Kelp or The Golden Dubloon will fill up your pet (not sure how much).
Strength:
There is an RE that increases strength.
Defense:
Scroll of the Warrior (+1-2?)
Movement:
Scroll of the Warrior (-1-2?)
Intelligence:
Scroll of the Warrior will not increase your pet's intelligence upon reading (note the description; verified it myself).
Potion of Brightvale Castle increases intelligence (by 1 point I think; found on IDB forum).