As far as I know, Siebel's DQ interface supports only Contacts, Accounts and Prospects for matching. I don't think it supports any other business components, including customized ones. If customized components are used, a customer would have to write and maintain their own integration with the EDQ services for key generation and matching. This has been done successfully in the past though I do not have any detailed information about it since it was a customization.
For matching using the standard interface, the EDQ documentation on OTN describes the workflow - see in particular the Siebel Integration Guide and the EDQ-CDS Business Services Guide. Please note that the workflow varies between Siebel versions. Only Siebel version 18.104.22.168 or later supports the use of the EDQ key generation services and the use of multiple child entities (addresses etc.) in matching. It also varies whether using Siebel CRM, or Siebel UCM. If using UCM, additional workflow steps occur in Siebel to invoke 'best record' survivorship etc. In CRM, matching just links new/changed records to existing.
No, there is a call to Siebel's DQ Manager (using the Siebel UDQ interface which is implemented by the EDQ Siebel Connector). The Connector translates the function call from DQ Manager into web service requests to EDQ, using the configuration stated in dnd.properties; this also 'translates' the hash maps of data into appropriate XML for EDQ. The EDQ Siebel Connector cannot be called outside of the DQ manager component. A custom integration could mimic what the connector does to call EDQ web services.