Refer to figure.
EASA learning objective 022.10.01.02.05 states: ‘Give examples of ATC data-link messages such as: departure clearance; oceanic clearance; digital ATIS (D-ATIS); controller–pilot data-link communications (CPDLC).’
EASA learning objective 022.10.02.01.07 states: ‘Describe typical types of CPDLC messages and the typical pilot work practices when requesting or accepting a CPDLC clearance.’

ADS-B; PF →  INCORRECT. Automatic Dependent Surveillance -Broadcast (ADS-B) is a surveillance system which uses GPS and a Mode S transponder to continuously broadcast an aircrafts position, altitude, speed etc to ground stations and other aircraft.  It does not send or receive ATC datalink message between pilots and controllers.

ADS-C; PM →  INCORRECT.  Automatic Dependent Surveillance - Contract (ADS-C) is a surveillance system which transmits an aircrafts position, altitude, speed and other information via datalink in accordance with an established ‘contract’ when requested by ATC.  It does not send or receive ATC datalink message between pilots and controllers.

FANS 2/A; PF  →  INCORRECT.  Communication between the aircraft and ATC is always handled by the Pilot Monitoring (PM) whether it be voice or datalink.  FANS2/B is the second generation future air navigation system technology which provides faster datalink communication than FANS 1/A.

CPDLC; PM → CORRECT.  Controller Pilot Datalink Communication (CPDLC) is a two way text based communication system between pilots and ATC which is used for non urgent communication instead of voice transmissions.  Communication between the aircraft and ATC is always handled by the Pilot Monitoring (PM) whether it be voice or datalink.

Air traffic control (ATC) messages such as ‘climb and maintain FL320’ have traditionally been passed via voice communication using VHF or HF.  Increasing levels of air traffic, especially in remote areas with no radar coverage, led to the development of the Future Air Navigation System (FANS) in the early 1980's. Its main objective being to allow more aircraft to safely and efficiently use available airspace, one of the key concepts of FANS is the use of datalink to replace voice communication between aircraft and ATC. 

First generation FANS systems are known as FANS 1/A and incorporate applications such as Automatic Dependent Surveillance (ADS) and Controller Pilot Data Link Communications (CPDLC). CPDLC is a system which allows two way, non urgent, messaging between pilots and air traffic controllers over the ACARS datalink system rather than voice transmissions.  CPDLC messages are mostly preformatted for standardisation but free text messages are also allowed.  When a CPDLC message is received it will be read out by the pilot monitoring (PM) in the sane wat that the PM handles radio communication with ATC.  It is however important that both pilots check and confirm CPLDC ATC requests and clearances and also CPDLC replies.