Hi there. Hope this helps:
1. Since we don't do the "selection" plan anymore, potatoes count how ever you want them to. Points are points, and we really don't assign them a category. They can be either a vegetable (but one 3 point potato still counts as a single serving of a vegetable, and you CANNOT count french fries) or as a carb if you're following the basic model of 6-8 points a day in proteins, and 6-9 points a day in carbs.
2. Chickpeas count as either a protein or a carb -- but again, it's more about the points. If you are a vegetarian, they would count more in the protein category -- but if you're eating hummus, it doesn't matter -- they count as the points you're eating and not necessarily limited to one category or the other.
3.

No. You cannot use V-8 splash, the fruit drink, as a fruit (or veg) serving. First of all, it's not all juice -- it's artificially sweetened, and has very few nutrients and no fiber. You can count regular Vegetable Juice v-8 as a veggie (as w/ tomato juice) but you can't count any fruit drink as a fruit, unless it's fruit juice. Period. Bummer. (by the same token, you can't count potato chips as a vegetable, either).