You have really exciting and interesting plans. Good luck with them!
There are many things that teachers are expected to do outside their contracted teaching hours. You usually have a contract for teaching a certain amount of hours; you need to add to that: planning time, time for marking homework and tests, meetings. Added to this, newly-qualified teachers tend to spend more time preparing lessons than their experienced colleagues do. In some cases there is also travelling time. If you work for a school that has corporate clients, you might be asked to teach one lesson in one company and then to travel to another company to teach a second class. If you have this type of job, you can expect to spend a considerable amount of travelling between lessons.
Of course things vary from school to school and from country to country. Before taking on a job check on all the aspects above: how much time are you expected to spend on all these aspects (expect to get add a couple of hours to any answer you get!) and whether the activities outside of teaching are actually paid for (though this is not the norm).
I think 3 hours of studying a day on top of a new teaching job is very optimistic. You could also look out for a part-time job. Having said all that, I’ve never worked in Korea; you could also post your question in one of the open forums to get the opinion of teachers who are familiar with Korea.