Don't know a lot about cat behavior. Would they hunt and kill a sparrow-sized kitten that wasn't theirs?

A male lion, when taking over a pride, will kill all the young lions that are not his offspring.

I have heard that lions' pack behaviour is more reminiscent of dogs than it is of domesticated cats, which have a more solitary nature similar to tigers or other big cats.

Do you know if this sort of behaviour has also been witnessed in wolf packs?

It's mentioned in Call of the Wild, but that's not a very reliable scientific source.

No; The social structure of Wolf packs is completely different from lion prides. Leadership is shared between a male and female (the alpha couple) who achieve their status independently from each other. Also, the pack includes subordinate males as well as females.

My understanding is that male cats are not necessarily good to have around kittens, even if they are the father, as they may see the kittens as future rivals.

That understanding isn't necessarily based on observed behavior or referenced studies though.

Infanticide is not unheard of in the animal kingdom...

> some cats will play with dogs as if they were a big brother.

I'd like to point out that this is an instance of you thinking of cats as small, stupid humans. Cats do not treat their siblings any different than other cats at the same age.

Indeed; that's the point I was attempting to make (though not very well). As far as I have seen, cats aren't afraid of a specific species, nor do they "identify" exclusively with only one specific species. If they find a dog (or a cat) who they can befriend, they do. If they find a large enough animal that scares them (I have a very tall friend), they'll run like hell and hiss whenever the animal is near. I'm not sure if they see classify species as much as they do friend or foe.