For a SE ATP it does NOT need to be done in a complex SE aircraft. The PTS will provide the practical test requirements. Plus a ME ATP can be done in a light twin aircraft. Any type rating you hold on your FAA certificate will be transferred over to your new ATP, with not Commercial Pilot limitations. The reasoning on that is that type ratings on FAA certificates are done to ATP standards. All the aircraft has to be capable of doing is the maneuvers and the approaches required by the PTS.
As for the SIC performing the duties of PIC under the supervision of the PIC is a very gray area. I would say that if you were not PIC typed in the aircraft, then the supervised PIC time, might not be valid. This regulation was written long before ICAO jammed the SIC type rating down our throats.
Concerning the oral exam, the big items are systems, emergency procedures, CRM, ADM and regulations.