I think they call those 'wind shears.' They have caused plane crashes, but not so often.
He also had the guts to get the skydivers out of the balloon. With the weight of five more people in the basket he would have had a much better chance of bringing it down. Very selfless of him to tell them to jump.
If you get hit by a downdraft, a parachute isn't going to save you. You're no safer with one than you would be in a balloon basket. If the downdraft is strong enough, even being in a plane isn't going to protect you.
Not usually. If the burner goes out and for some reason cannot be reignited, the balloon acts as a parachute and descends at parachute speed (about 17 feet per second).