This one answers many questions:
https://www.backyardchickens.com/th...rmation-aka-button-quail.420619/#post-5137331
I aggree with most of what Fishkeeper says (not sure about the hamster thing though! ^^) but would like to add that mine completely ignored my cats, as long as the cage was a box style cage that was only open (with wire) on one side (not the top) - the cats could climb around on the wire and the quail would barely look up. It's true that cat saliva can kill birds, but it needs to get into a wound to accomplish this - my cage (self built) had a board at the bottom and then wire above that and the wire was so small the cats couldn't fit their paws through the holes, so the birds would have to jump into the wire for the cats to stand the slightest chance of even touching them.. I also find that buttons quickly get used to loud noises. A chainsaw working a few meters away is no issue at all, once they've heard it a few times.
With regards to breeding, some buttons go broody every time they have 5 eggs, some never go broody at all, so you might need to incubate the eggs if you want chicks.
If you prefer the natural way, big cages with lots of cover improves the chances. They like making their nest in hay and in places where you can barely see them, so a little hay behind a spruce branch or artificial plant in an enclosed corner of the cage is often where mine nest.
Any specific questions, ask away.