You can be at a healthy weight and still develop diabetes. I think the whole health discussion is about more than just weight.
Yes. Weight is a symptom, not a cause.
Eat too many carbs/sugars -> more insulin which yields more body fat.
It matters in weight loss, without a doubt and weight often matters in a lot of these arguments about what is killing you. I don't think you can equate weight and cholesterol though.
With regards to weight-gain, yes. Not overall health. You'll get yourself diabetes maintaining that kind of sugar consumption.
Ah, good to know the first law of thermodynamics is still in effect, thanks!