The form is I-485, and an SSN is not required to file.
What is required is listed in the I-485 instructions, and you can follow this guide as well > http://www.visajourney.com/content/k1k3aos
VJ also has example forms you can look ovr as you fill out the forms.
Information about the vaccinations and whether or not you need a civil surgeon and an I-693 > http://www.visajourney.com/forums/topic/428381-i-693-report-of-medical-examination-and-vaccination-report/?p=6206232
You do not need a an unexpired passport for approval of AOS, EAD and AP. However, AP is used to re-enter the US when traveling abroad, and you need a valid passport to use when traveling.
