Absolutely no. First of all he can't just come live in the US. He needs legal paperwork.

He won't be able to work. Even if you marry him it will take awhile to obtain green card. In a meanwhile he wont be able to work. So who'll support him? You live with your parents. Will they support him? Would they even allow this stranger to move in? I doubt they would. You don't know him, so how do you expect to share house with him?

I also don't buy his story about sheets separating sleeping areas. Maybe this guy lives in this bizarre ways but it's not a norm in Hungary. Sure it's not a wealthy country but people don't live with sheets instead of walls. Dude tells you sob stories.

Absolutely no to him buying one way tickets to the US.

I worry if you allow it and this guy just shows up it will be hard to get rid of him. He'd say he has no money to go back to Hungary. It's going to be a mess. Your safety might be in danger.