I am not sure exactly what is required for an alien registration card. Usually, as has been my experience, the school that employs you as a teacher will be responsible for getting your alien registration card. I believe that once you are in Korea with a signed contract and an E-2 Visa, it is a given. The school will then have the information needed except they will also probably need your passport when they go to apply for your card.

As for the requirements for an E-2 Visa, you will need a Visa Application Number to apply for an E-2 Visa. This numb er will be sent to you by the hiring school once they have submitted all of your documents to Korean Immigration and everything has been approved. You can then apply to the Korean Consulate here in the USA. The Consulate will send you 3 forms to complete (one of which is a self-check health form), a passport size photo, a copy of your college diploma notarized or a sealed copy of your transcripts from the university, and a $45 fee for the visa. If you talk to someone in the Korean Consulate's office, they will email you a list of information they need for your E-2 Visa. You cannot get an E-2 Visa until you have a signed contract from a school and have submitted your required documents to the school for Korean Immigration approval.

I hope this helps some.