I installed Oracle's REST Data Service using DB SYS user,
After the installation, will SYS user be used while running Oracle RESTful Data Service?
The required timing was at the time of command execution
java - jar ords.war install simple
When running ORDS it use APEX_LISTENER, APEX_PUBLIC_USER, APEX_REST_PUBLIC_USER, ORDS_METADATA, ORDS_PUBLIC_USER depending are you using APEX or only RESTful services
No. The sys user is only required for the installation.
In fact most of the installation can be done using normal DBA privs. However some small parts requires SYS. I think for example setting the new apex version in the registry (dba_registry) require sys privs (my personal guess).