(Spoiler) plot questions

While I found the movie riveting, some things just don't make common sense to me:
1-why would Burke select the sharpest guy for the investigation? I'd pick a doofus who'd muddy the waters or get easily thrown off. I know some suggest because Burke wanted someone who could be manipulated, but, geez, that seems to add a layer of risk hardly needed if you pick a doofus. And in the initial training session, Burke rebuffs Clayton's attempts at direct mentorship; "You're making a mistake." "I'm not your friend."
2- why would Burke even voluntarily offer a gun for Clayton's use. Why not let him 'become a star on the wall' so the investigation ends in failure and you have to start all over?
3- at the station chase, Zach gets the drop on Clayton, merely pushes him down, and flees...only to then re-engage in a life or death gun battle. What could possibly be the plot justification for not killing...or at least incapacitating...Clayton when you've got the chance..knowing Clayton's going to just get up?
Still loved the pacing of the movie, and the superb acting.