Regarding the confusion, if this is for your thesis like your previous question, ICAO Doc 10037, which supercedes Doc 9694, should clarify many things. But there could be more applicable references based on your research topic (you can ask your advisor to make recommendations).
Regarding your questions:
Does FANS 1/A have ADS-C?
- "FANS 1/A" and "FANS 1/A+" have CPDLC and ADS-C
- "FANS 1/A ADS-C" has ADS-C but no CPDLC
If it does not, what is used for position reporting to the ATC?
CPDLC using FANS over ACARS can be used if ADS-C became unavailable (Doc 10037 § 126.96.36.199.3 and Doc 007 § 6.1.32). ADS-C is mainly about automatic reporting based on fixed intervals and events. Otherwise the reports are submitted manually (voice or CPDLC). Example from ATC from Doc 10037 § 188.8.131.52.3:
REQUEST POSITION REPORT
ADS-C HAS FAILED
Is satcom used in the FANS 1/A as a message-transporting service?
Yes. The available subnetworks are: VDL M0/A (aka Plain Old ACARS – POA), VDL M2 (AOA), HFDL (high frequency data link), and SATCOM (Inmarsat and Iridium).
FANS 2/B has LINK2000+ CPDLC and ADS-C (...)
Actually, that's FANS C. It includes both CPDLC (LINK2000+ / ATN-B1) and ADS-C. It made its debut recently.
I think you are confusing position reports, with ADS-C. While ADS-C provides position reporting, it is not the only way, as explained earlier.
What is the role of FMS?
There isn't one blanket answer.
An FMS is where all the position sources feed, whether the FMS can distinguish between mandatory reporting points, and whether it allows the position to be overwritten by the crew, it depends on the aircraft and the installed FMS.
For example for the Boeing B737, B777, B757, B767, B717, MD90, MD10, MD11:
The FMCs on these Boeing aircraft do not distinguish between ATC mandatory waypoints and FMC sequenced waypoints for position reports. However, the FANS 1 of these aircraft will allow the flight crew to overwrite the FMC- determined default "reported waypoint" position and time.
Source: Doc 10037 § C.5 FMS processing of waypoints in position reports