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?
Only "FANS 1/A ADS-C" does, if "ADS-C" is not in the name, then no. Applicable standard is DO-258A/ED-100A.
If it does not, what is used for position reporting to the ATC?
ACARS is used. ADS-C is mainly about automatic reporting based on fixed intervals, for example. Otherwise the reports are submitted manually – like making a position report via voice, but instead via ACARS (which is supported by FANS 1/A).
Is satcom used in the FANS 1/A as a message-transporting service?
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