Overstun can happen if you hit someone abit way too much, this happens if you hit really wounded enemies with stunweapons or if you overwhelm a healthy enemy with superior stun weapons. Overstun can also happen if the enemy falls unconsious in smoke as he will asphyxiate. You can remove overstun from friends, allies and foes via medkits or painkillers.
Close Range Combat works by some parameters, targets and attackers reactions, energy, melee accuracy and weapon type. Generally, pistols have the best chance to shoot someone in the face, the longer the weapon is, the more likely it is to be parried to the side. By the time Sectoids will appear, your agents will be bordeline unkillable at point blank since they will in 9/10 move their weapon away so charging them isnt that bad of an idea if you know there arent more of them around the bush.
Also, CQC will activate even if you are shooting at someone else but there is somebody next to you... they wont let you shoot at their buddies.
No, AI cannot run hit the gas to conserve TU at expense of energy. Dogs and Rats can run and this will be esential so they have as many TU as possible when you get them next to a door or corner. Dogs in particular can maul most enemies and their teeth has actually some large damage output and they can also bark at enemies to shred their TU so if you position him behind a door and a baddie comes in the dog will drain all of his TU and he wont be able to act at all and if he aproaches the dog in proximity (like the dog is directly next to a door the dog will bite him. This bite can take down most human enemies in 2-4 attacks and the bite is really cheap time unit wise and somewhat accurate.
There events are bound to happen, good or bad, removing certain factions from play will delete some of these but for a good chunk of the game, if the game throws alot of bad events at you, you need to do extra work to get a good rating and increased funding, how much the game shits on you will tell you how many extra miles you will have to jump.