Do I have to re-buy?
I had a Minecraft account and I wanted to change my skin, but I didn't remember my answers for the question. So I made a new account, but I can only play the demo, even though I had already bought the game. What do I do? Do I have to but it again?
You don't need to re-buy the game, just continue using your old account.
If you can't remember the answers, contact mojang support with your transaction ID, so they can reset them for you.