Yes there are multiple reports of leopards hybridizing with jaguars in captivity. These two big cats are not each other's closest relative, because both are more closely related to the lion than they are to each other. The leopard is the likely ancestor of the lion, and the jaguar in turn evolved from a population of the lion in North America.

yes. tigers, lions, jaguars, and leopards can all be interbred. mind you, they aren't necessarily healthy hybrids. i'm not sure about all the combinations, but anything with a male lion as the father will get too huge for its body to handle. this is because of a part in the lion's genetics. it encourages growth in the womb, but is later nullified by the lioness' genetics. no other female cat has this, so there's nothing to stop the cub from growing

Yes

They wouldn't breed naturally. But in captivity i'd assume they would!

If they can, are the hybrid offspring sterile? How closely related are leopards and jaguars? Tigers and lions have been crossed into sterile "Ligers", but the leopard and jaguar look fairly similar, but live in different continents.