If you got teammates that you don't get along with, you probably have much bigger problems than them "stealing" your loot or kills. There is no need to artificially limit interaction between teammates. Try to get along or move on to the next game if you can't.
Both suggestions are bad.
For deathboxes: what if you WANT to give something to teammate and you need to do it fast (you're being ambushed)? You take that shield cell yourself and drop it to the ground for him to take? And what if you're already knocked and he desperately needs that heal, armor or weapon? I see only problems with such "locking" and absolutely nothing good.
It's hilarious when teammate that didn't even participate in the fight comes rushing to grab that lvl3 armor from the box while you revive the other teammate, but that's just part of the game. Such teammates usually don't mark good items and hoard items they don't need and never share either (they drop what they don't need somewhere in a ditch so that you don't see those items) - you will rarely win games with them anyway. And if you all participated in a fight, well getting the kill doesn't morally make the loot yours. If they feel like giving you first run on all of the loot, good for you, but if they don't - they are as entitiled to the loot as you are.
For kills. It's kind of in the description. Whoever kills the enemy (meaning gets the last hit), gets credit for it. It would be really awkward and nonsensical if it was otherwise. That one single last hit can sometimes involve a lot of effort, much more compared to the other part of damage done (when victim is running away, trying to heal or leading you to his teammates, etc.). There's no measure to determine who "deserves" the kill credit more, so simple is best - get the killing blow = get the kill credit.
