Vitamin supplements are probably helpful only when you have vitamin deficiency. Surplus of vitamins does not likely help.
Antioxidants work in the laboratory, but to this point, as I know, the actual health benefit of any antioxidant has not been proven.
Yes, drinks with antioxidants are good for you. (:
Nobody knows. Research isn't easy to do in a way that would settle things -- different studies don't use the same products, and not all products are equal, and people don't absorb things the same way. Most of medicine is an experiment with us as the guinea pigs because we just don't know as much as we'd like. You just have to make a decision in this area and see what happens. What's most important is your diet -- a varied diet high in colored vegetables and green leafy vegetables goes a long way to doing what vitamins are taken to compensate for, but most Americans don't eat that way. Some people have special needs for more of something, some don't. Some are just covering their bases as best they can. As for drinks, if they're high in sugar and other things besides the antioxidants, they're not worth it. The best "drinks" for antioxidants are green tea, of course, but otherwise the best are to juice it yourself so it's fresh and contains as much pulp as possible.