Have you ever had one player kill another player's character, take his stuff, abuse him because his player character was more powerful, etc?
When one character really
would kill another character, or take his stuff, or abuse him, yes, we've had it happen. Rather a lot, when I'm GMing, actually, because of my famously loose style of GMing.
If so how do you handle it? Do you allow PvP and just tell the player with the 1st level character always being pushed around by a 12 level character "Too bad" or what?
Our characters tend to be more-or-less around the same power level, although that's often eclipsed by the fact that some of our players are better than others. Everyone at the table knows this can and will happen, though, so no one's really troubled by it, as long as it's in-character. [That's what we're at the table for.] Is there sometimes resentment when one player is more clever than another, and triumphs because of it? Of course, but to our minds, the solution is simply to become more clever.
We also bleed off some of the excess desire to kill each other by setting aside some time at the end of the session for out-of-continuity blowing the crap out of each other, famously named Omnidrome by my GM. This not only hones people's combat skills, but lets them get the better of each other in a way that doesn't disrupt the campaign.