1) you need make appointment through InforPass in USCIS for the local CIS AP application. Do it as soon as possible.
2) bring the I-485 receipt. And filled in I-131 (download from CIS website) and required documents in instrution( 2 passport pictures, passport, legal stay document, et al).
3) bring documents indicated that your father is in critical situation. A statement from hospital signed by the doctor should be OK. FAX is OK. A notorized translation will be better. Ask your friend translate it, then bring him together to swear under notorization officer in some bank.
4) you can get it in one day at local office.
5) for backup, you can still fill AP by mailing to USCIS. It may take more than 1 month. Just balance by yourself.