Running form question?
It probably would negatively affect your performance. Straining your neck would put your body into a weird and aerodynamically inefficient posture.
Yes, it almost certainly would since your head being tilted back is going to affect your balance and probably throw off your center of gravity, not to mention increase the chances of injury since you'd no longer be paying attention to what's ahead of you (what you're about to run over or through) or anything that might be approaching you that could strike you. You'd be safer running blindfolded because at least your balance wouldn't be impacted.
It will if you run into a tree.