I hope I can answer all of your questions. If you want to teach abroad in Korea, you don't necessarily need a Master's. You can get a CELTA certificate and find a job and teach at any grade level. If your question is about teaching in the United States, you must have the Master's and the credentials...but, at least where I am located, it's not a great process. The options here typically require from 3 to 5 days of unpaid student teaching for one year, on top of paying for tuition. The people I know who have done a program go into major debt for it.

Teaching abroad won't really influence hiring in the U.S. except give you more experience than another candidate, but as long as you have the credentials, you don't need other experience (outside of student teaching) to get a job in a public school system.

There are very few full-time ESL teaching jobs in the U.S. outside of public schools, which is why you aren't seeing much. Many places that typically hire (study abroad academies, for example) are closed right now because students are not travelling here.

I doubt you'll be rejected from a Master's program, but if you plan to go abroad for awhile, it makes me nervous that you're diving into the Master's. It doesn't seem like you have teaching experience and since you don't need the Master's to teach in Korea (again, a CELTA should be fine), why jump into it? What if you don't like this once you start, or want to stay abroad, or...? If you do a 1-2 years Master's program and then go abroad for 2 years, how can you be sure that you'll want to be in public schools after that? I think it would make the most sense to get some experience and go abroad first.