How often (real time) should one feed one's pet? And when they are released from the stables, are their bellies full or do they need to be fed soon?

I use animal lore to tell me when to feed 'em - I prefer to keep them wonderfully happy In theory, the stable hands are supposed to keep them fed while in the stables, but at a measly 30 gold per week, it's probably not top rate kibble!

as long as you have the correct taming and lore for them to listen to you every time, there should be no reason to feed them once they bond.... i would definately check them if they dont seem to be listening well to you though... dont want them returning wild on you at an inoppurtune time

im pretty sure that every time they respond to a command they gain a happiness level... which is why if they always do what you tell them to they should always stay wonderfully happy.

Also the further you walk away from a pet the lower its loyalty will become. The higher level pets drop loyalty quicker than lower level tames. So if you recall away from your pet and return later; feed it when you return.

Also remember that humans get the 20% Jack of All trades (JOAT), making it possible for ANY human (regardless of taming levels) to use Animal Lore to tell you the state of pets loyalty. It may take a few tries, but works well.

Over time, though, if you don't feed them, their happiness level goes down. You can't just feed a pet once for bonding then never feed it again. It'll get extremely unhappy, which causes it to start ignoring your commands and eventually go wild.

Here's the UO.com playguide info on the topic:
ORIGIN - Ultima Online - Playguide

hmmm havent fed my mare or my rune beetle in probably 2 years... they both are still always wonderfully happy... mare im always on but my rune beetle stays in the stable untill i need him.... interesting topic

If they stay in the stable, the stable hand feeds them

It's as you use them for fighting, or even just riding them for lengths of time, that makes them need more food to keep up their happiness.