What is the ideal diet for donkeys of their ages?
The appropriate diet for a donkey is grass or hay. Donkeys have very efficient digestive systems; they come from parts of the world where forage can be pretty sparse. Some donkeys seem to get fat on little more than air
and that's a problem. Donkeys can develop deposits of fat on their necks and rumps that are almost impossible to get rid of. While donkeys love sweet feed, if you must give them feed, it is better to give them something that contains lower, slower delivery carbohydrates than sweet feed contains.
How do you tell the difference in breeds (if there are)?
There are a few donkey breeds; the main difference with most of them is size (Mammoth and miniature, for example). There are a couple of breeds that are distinctly different, but you kinda have to know what you're looking at to know what you're looking at with them. There is one breed with very long hair, but it is a pretty rare breed.
How do you know if they are being friendly or wanting to bite?
As with most equines, the ears are a good indicator of what the animal is feeling. Those twin exclamation points on a donkey's head are hard to miss! The ears typically point toward whatever the donkey has its attention on, so if you are behind him, his ears may point toward you. That is quite different from the ears going flat back against the neck as a sign of displeasure; it won't take long to know the difference.
Where do they prefer to be petted?
If a donkey doesn't know you, you want to keep your hands away from its face at first. "In your face" reads as aggression to a donkey, and he'll try to avoid it. Petting/scritching on the withers/shoulders is usually understood to be a friendly gesture. Once the donkey is comfortable with you, he won't have a problem with having his head petted. Some people have this thing about grabbing a donkey's ears, so a lot of donkeys are protective of them. Donkeys that have been handled with kindness may even enjoy having their ears stroked, but you mustn't pull on them (remember that when haltering them, too. They make special donkey bridles with a buckle behind the ears to avoid this.
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What sort of grooming do they need? (One has a really fuzzy look to it, the other seems to have shorter hair)
A good going-over with a brush is all the grooming a donkey should need. Donkeys need hoof care like a horse does, but the angles of their hooves are different; you'll need a farrier that is familiar with donkey feet.
Donkeys grow longer hair in the winter and shed it out in the spring, so it may be that one of the donkeys just hasn't finished shedding out yet. If the shaggy one is the older gelding, retaining his long winter coat could be a sign of Cushings, too. Donkey hair doesn't shed water like a horse's does, so shelter from the elements is even more important for donkeys.
Enjoy your new long-eared friends!