probably better off to just continue through the story. it’ll hand out your new upgradeable (legendary) weapon, basic legendary accessories, and your SS (soul shield) set, as well as a bunch of other materials. if you do decide to get the lv. 60 voucher, just save it for now. else you’ll be missing a whole lot of the story.
haven’t tested that, but i’m assuming it should work, though i wouldn’t know why you would do that. after all, the badge exchange doesn’t exactly highlight WHICH badge you need, to trade, just that it’s a legendary mystic badge
they don’t unlock skills anymore, but they do give you points you can use after you awaken your class. so, yeah, you should still get them and use them.