The person dealing the most damage to an enemy will get stilghtly more experience points from a battle. It has NOTHING to do with who gets what drops or how many items drop. I've been the damage dealer in plenty dungeons where I'm the only one who got nothing good. And I've also been on the other side in some battles where I couldn't get a shot in but I still get great item drops. It's all just luck of the draw. The only requirement for a boss item drop is that you be in the battle and survive.
That is false. So long as you are alive at the end of the fight, you will get rewards for the fight. Whoever deals the most damage doesn't matter, so you don't have to worry about that.