Anyone know how long it takes for a pet's hunger bar to empty? And whether every food item reduce a pet's hunger evenly?

IIRC, pets lose 1-2 hunger every hour or so, and yes every food reduces hunger evenly. If you're looking to feed for Gourmand, I never paid super close attention but I was always able to feed my pet the full 10 items several times a day, if I remembered.

Pets will eat any food you give them if they're at all hungry, their reaction is purely random. It's possible foods have the same value, or that they get hungry at the same rate, but not both. The difference in time is small, though. This random bit is determined each and every time you feed your pet and has nothing to do with whether the pet has eaten the same food before or what it's nutritional value was before. This results in being able to feed a pet from 8 to 10 items in any eight hour period and why you'll often see people say from 1-2 items per hour. I think is lucky to always get 10, I have Gourmand and it was more variable for me.

I found it useful to Lock the next foods in queue in my Inventory, that way even if my eater didn't get to the food I had planned, I don't forget. Backchecking eaten foods vs Account Search or the Foods Eaten list can be hugely time-consuming otherwise.