Peanuts are legumes/nut-esque peas and cashews are fruit from a biological perspective, sure, but like the claim that strawberries, raspberries and blackberries aren't berries, but bell peppers and bananas are, it's just a case of the "official" definition being wrong rather than the average person
They're called that because they are the size of grape seeds. Why anyone thought that made them appealing is beyond me. Grape nut flakes are pretty good though
I thought it was because the guy who invented them called glucose "grape sugar" because cereal people in that era were entirely detached from reality, and he thought they tasted nutty. And that baking the cereal released glucose.
Can't say I've heard of grape jelly either. When you say jelly, do you mean jam? Or are you talking about the wibbly-wobbly stuff that kids love? Because I dunno how you'd put that into a sandwich