(1) Do I need a degree in English in order to teach English?

No. You will likely be teaching functional/conversational English and not Shakespeare or Academic English, so a degree in anything is absolutely fine. We can even arrange for you to obtain a degree in a fast-track timetable, along with your TESOL/TEFL certificate. The certificate is your teaching credential and indicates that you are qualified to teach English as a second language since the training focuses on pedagogical technique, ice breakers, and lesson planning.