You taking online classes in relation to back home doesn't really matter in Korea. The H1 is for you to come to Korea, experience it by traveling around and work part time to fund these travels. You could come here on an H1 and not work at all, or not travel at all. But it is meant for the reasons of which I mentioned. You need to write an approximate Holiday plan when applying for the visa, ex: 1st to 3rd month I will travel to/around X Y Z and do A B C. This does not have to be fully followed but just approximate. Save 2 copies of it because you will need it when applying for the visa as well as the Alien Registration Card once you are here.