I think that white potatoes, corn, and other dried beans belong more in the starch category than the vegetable one. (Yeah, dried beans are more of a plant-protein, but not really what people need from fruits and veggies.)
Yes. The state of foods (dried, canned frozen, fresh etc) does not cause a change in its nutrient content. It’s the additives and/or preservatives that raise calories or lower nutritional value. Calorically and macro-wise, they remain the same. Additionally, there’s not a difference between “starch” and “vegetables” in the way you’re saying. Vegetables can contain starches. Starches are a type of carb as are sugars and fibers.
https://medlineplus.gov/carbohydrates.html
https://www.harmonyhousefoods.com/blog-nutritional-value-dehydrated-veggies