1 ) The private interfaces will be used for the private network (using a separate path) which carries traffic for synchronization and MDS.Public interfaces are used for public network which carries traffic between each side of the synchronized system and foreign systems.eg router to CVP etc.
2) You can use procmon to query information indirectly from the Automatic Call Distributor (ACD) of your site. The Cisco Intelligent Contact Management (ICM) processes that reside on the Peripheral Gateway (PG) allow you to:List agents, skills, services, increase tracing on ICM ,query ACD functons.
OPCTEST will give the current picture of which side node is active and which processes are running and their sync time so it basically health check of the system.
3) I believe for communication and synchronization only TCP is used as UDP is used for RTP.