Tl;dr: If you know what kind of apple you're looking at, you don't need to test the apple.
I don't think you can tell any of those things about an unidentified apple without destroying it somehow. You can tell how hard/soft it is by pressing firmly, but this will leave a dent in the apple, so that may or may not count as destroyed for you.
However, if you know what variety of apple you're looking at, you can know these types of things without even touching the apple, as each variety has its own characteristics regarding sweetness, crispness, juiciness, and other qualities. For instance, Honeycrisp apples are typically very sweet and crisp (as the name implies) and are excellent for eating out of hand. You can find more information about different varieties of apples here. Grocery stores (at least in the USA) typically label their apples by variety. If you shop at a farmers market and the varieties aren't labeled, the farmer/seller can usually tell you (if he can't, I probably wouldn't buy from him anyways, but that's just me).
As far as durability goes, that is largely dependent on how you store your apples. Refrigerated apples last longest, as they do not continue to ripen in the cooler temperatures of the fridge. They will if left on the counter, though, leading to mushy, rotting apples in just a week or two. (I have successfully kept apples in my refrigerator for several months, though those were fresh-from-the-orchard apples, so your results may vary.)
Nutritional content varies by variety as well, though I was only able to find a single source focusing on vitamin C. However, as vitamin C and potassium the main nutrients in apples, that may be sufficient as far as varietal differences go. You can find some more general nutritional information for apples here.