They are both correct, but we would normally say "young and beautiful" not 'beautiful and young" If it were describing a noun, it would be "she's a beautiful young woman" because "beautiful" modifies "young woman"

Both are correct! When multiple adjectives in a list describe a common noun, they can generally be rearranged and still mean the same thing. As for your last sentence, it's technically correct but doesn't sound the most natural. Instead, most people would probably say something like "you're all equally beautiful."