Hello Carlos Francisco Chavarría Rustrián,
the ports used are highly dependant on your environment and if you changed default ports or not. Also, older versions of DocuWare require more Ports.
(Everything here uses TCP)
In your scenario, all your IIS-Servers (AAR and all DW Backend Servers) need to be reachable via http and/or https, default 80/443.
the Fulltext server operates on 9012 (in default), which needs to be reachable by all DW Backend Severs and all DW Frontend Servers (AAR).
Authentication Server runs on all Frontend and all Backend Servers on port 9000 and needs to be reachable from all other DW servers.
Content Server and Workflow Server run on all Backend Servers on Ports 9001 and 9002 and need to be reachable from all other DW Servers.
The Oracle Database operates on 1521 in default, which needs to be reachable from all DW Servers.
What do you mean by "Server API"? Do you mean the DocuWare REST API or another piece of software?
In case of the REST API, it is available on the same ports your IIS uses for the DW WebClient.
If it is another software, please contact the vendor.
Greetings from Germany,
Simon H. Hellmann
DocuWare System Consultant