can I buy Sephora's gift card from those websites and pay fragrance costs with that while being able to send those fragrance on any US adress?
Not sure - I've never used a Sephora gift card before. If you pay for the whole order using a gift card, and don't enter credit card details at all, then there's no reason you couldn't have it shipped anywhere you like.
I've never used purse.io because I read reports about the people buying on your behalf using stolen, hacked, or otherwise illegitimate credit card details, and users having their Amazon accounts closed or even their address blacklisted because of it. Don't know if that's just scare stories, but I use Amazon a lot and having my address banned would suck, so I've never risked it.