how can i join the peace core or something similar so i can travel for free to Korea?

If you have a degree you can teach English. Even if not you can do programs for the summer. Also if you want, contact your local social services agency and you may be able to pick up babies that have been adopted by couples in your country. They will pay your roundtrip airfare. Most language schools pay airfare or offer reimbursement. Check out ESL jobs on Google and go from there. Teaching jobs come a dime a dozen over here.