I actually have heard this before--so I think it does work. You're supposed to drink it before every meal that you have. 3xs a day I believe. I think I am going to try this as well! : )

No...and yes. Here is the problem with it. In this "diet" you drink a glass of the juice before any meal. This helps fill you up, and thus you eat less. But fruit juice has a lot of empty calories in them, and it would be a much better body investment to just eat real healthy foods. You could do the same with water, and not consume any calories.
Grapefruit does have an enzyme in it that makes you feel fuller longer, but this is not in the juice, it is in the flesh of the fruit, which is actually just fiber. There is however something that will make you lose weight the more you do of it, it is called exercise!) The truth of the matter nothing you can consume will make you thinner. Sad but true.
If you want to lose weight, your best approach is too eat planned smaller meals throughout the day. Foods low in fat and calories, and high in fiber are filling foods that help keep you full longer. (examples of such are lean meats like grilled chicken breast, grilled fish, and lots of fresh fruit and veggies. Also whole grains, get rid of "white" starches, they don't fill you up, and have been known to cause cancer.)
The word "diet" should be banned from our vocab entirely. They don't work. You have a 96% chance of gaining all the weight back. 96%!!! Why bother?

it does

This is questionable but it is good for you reguardless. It has alot of healthy benefits, so what can it hurt as long as you stay within calorie intake range. I recently started drinking it myself, we'll see what happens. It is only 70 calories for like 5.5 ounces.

No...it makes it harder.

no, reducing calorie intake and increasing exercise is the only way to lose weight

No it actually hinders weight loss because of the added sugars in the juice. Stay away from calories in liquid form...it's wayyy too easy to overconsume your daily caloric intake that way.

The high citric content will help eliminate some water weight. It acts as sort of a natural diuretic, and it is high in antioxidants.
There is a difference in the type of sugar that fruits have vs. the sugars in sweets and processed foods. You should eat a few servings of fruit every day. You can count an 8oz glass of pure fruit juice (not from concentrate) as one serving of fruit. Tropicana and Simply Grapefruit are good juices that are 100% juice.