I don't really know much about the types of damage myself, but I've looked into it for my DPS Mercenary in the past, so from what I've read, one aspect of choosing your type is depended on the skills you use. If you have a rotation with a couple of skills that do a certain type of damage, it makes sense to go look for items with that particular damage type boost. Also, a quick info check on these types, it's internal and kinetic damage that penetrate armor, not elemental. By the way, internal damage works on droids too, I think. At least my DoT Gunslinger had no problems applying internal damage on droids.
On your second question: there are stuns that work on elites and champions, yes. Most won't, but there are some. My Jedi Guardian tank has a stun that both raises threat and can stun even champions, yes. But, depending on the (advanced) class and skill tree, be restricted to probably maximum one.