Your first problem should NOT be happening. If you're seriously shutting it all the way, and it just randomly pops back open, take it to an Apple Store, most likely you'll get a replacement unit.
Second, ALL PBs do those exact things upon waking from sleep; it's not a problem at all, it's just how it is. Obviously AirPort turns off while asleep, thus it has to re-engage and find the network again once it's opened, and that takes a second or two, what you described is perfectly normal.