Sounds like he is a tenant in your house. You made an agreement with him that he could live in your house in exchange for payment. He's paid up until June 2. You cannot kick him out. In fact you cannot kick him out on June 2 unless you have a contract stating that he leaves on that date. He is a tenant and you have to go thru legal channels to evict him. First you give him a 30 day notice.
Call an attorney that deals in landlord/tenant issues and ask. Many attorneys will answer questions without a charge for the first consultation.
You can also call the District Attorney's office for the county and ask to speak to someone working in the civil section that deals with landlord/tenant issues. Either attorney can verify for you if this a renter issue and how you could get him out.
I suggest that you just wait it out for another 2-3 weeks. I understand you being angry. Actually, I don't understand taking in a teen or young adult who isn't going to school. If he is an international student at a school then you can ask for help from them. I don't know what they can do but it wouldn't hurt to ask.
Have you tried just asking him to leave. I'd willingly give him a refund to get rid of him. I'd have done it a long time ago. If he's been this way for months, I wonder why you're just now looking for a way to get him to leave.
BTW: What you've written doesn't seem so bad, except for maybe breaking the microwave. Did he do it on purpose? I sometimes forget to flush my toilet. My daughter put a can of soda in the freezer and it exploded. How old is this student? She didn't do a good job of cleaning it up, either.
Just as with your own child, you should've had a written agreement with him outlining the boundaries you would enforce in your house once you realized you didn't have similar housekeeping standards. A part of the agreement would've included him leaving if he didn't meet certain requirements. And then I'd have asked an attorney if this would've worked.
I suspect you're angry at yourself too. Consider this a very painful lesson learned. You're only raising your blood pressure and making life unbearable if you continue with this degree of anger. I really think there is nothing that you can do at this late date.