The recent players list is broken, it will randomly update one new person to the list once it's "full" or something like that.
As for the prestige challenges, I think that it won't reset the chopper challenges neither the sentry gun challenges on the "Prestige".
Never really paid attention to them and no need for me to prestige anymore.
Yes. The recent player system is crap. When you prestige, it does reset the challenges, but it keeps any titles or emblems you earned for those challenges. Still, this is good for you. You get all those challenge bonus points again to help you level up faster after you prestige. So, you can go and jump in the well in Seatown again for some easy points.