To which security domain does the Cabin Intercommunication Data System (CIDS) belong?
As the commentators above pointed out, there are some issues with your question due to the concepts involved.  

As @Bluephoenix mentioned, the security domains are defined in ARINC 664 Part 5. These domains specifically apply to ARINC 664 networks, though the concepts can be applied to other networks.  

You also reference a Cabin Intercommunication Data System (CIDS) which is an Airbus specific system in the A320 series -- which does not have an A664 network. But we can look at its functions to see which domain would apply if they were implemented on an A664 network.  

The A664P5 descriptions are:


  Part 5 describes the objectives, characteristics, services and
  functions that should be satisfied and provided by the aircraft
  computing network as a whole. Their allocation to specific networks
  and devices is the responsibility of aircraft network designers and
  specified by other documents.
  
  The Aircraft Control Domain (ACD) and Airline Information Services
  Domains (AISD) can be divided into sub-domains.
  
  The ACD can be divided into two Sub-domains:
  • Flight and Embedded Control System Sub-domain, where the aircraft is
  controlled from the flight-deck
  • Cabin Core Sub-domain, which provides environmental functions
  dedicated to cabin operations, such as environmental control,
  passenger address, smoke detection, etc.
  
  The AISD can be subdivided into two sub-domains:
  • Administrative Sub-domain, which provides operational and airline
  administrative information to both the flight deck and cabin
  • Passenger Support Sub-domain, which provides information to support
  the passengers
  
  Subsystems within the Passenger Information and Entertainment Services
  Domain (PIESD) could be supplied by different suppliers.  
  
  Passenger Owned Devices (POD) can be supported by onboard networks.
  The Passenger Owned Devices Domain (PODD) is constituted of only those
  devices that passengers may bring on board the aircraft.  


Reviewing the CIDS documentation of functions and comparing it to the A664P5 definitions, it would appear that the CIDS has functions within the ACD Cabin Core Sub-domain (environmental control, passenger address, smoke detection, etc.) and AISD Administrative Sub-domain (operational and airline administrative information to both the flight deck and cabin.)  

To your last question, ACARS is a legacy communications link designed to support Airline Operational Control (AOC) and Airline Administrative Control (AAC) messaging.  With advances in data link systems and applications, ACARS can refer to either the AOC messaging (most correctly) or the entire data link system (not so correct) which also includes Air Traffic Control (ATC) messaging.  

The ATC portion of data link falls under the ACD. AOC and AAC messaging fall into the AISD. In the case of the A320, the CIDS does not have a direct interface to the AOC/AAC messaging. These messages (manifests, gate assignments, etc.) are printed out in the cockpit and passed to the cabin crew as needed. On some newer aircraft, this may be accessible by the cabin crew via a terminal.