Hi,
after re-reading the original question I found that there are some more questions to answer.
I hear that different ospf processes in the same router maitains different topology databases and that by default, the processes do not communicate or exchange routing updates.
This is correct, different OSPF processes are "ships in the night", even when they are running both in the global context or in the same VRF.
I also hear that by default, OSPFv3 processes use the same multicast address and the same UDP port number; meaning that all the processes in the same multicast group and using the same UDP port number can exchange route updates.
This is also correct, in OSPFv2 this is also true when the interface network type is broadcast-capable.
How do the above two default behaviors match up?
Well, there has to be a source too, and the IP-interface of that source has to belong to a certain process.
1. The multiple OSPFv3 processes in the same router populate the same routing table right? Which of the processes will perform the best path selection procedure? If multiple OSPFv3 processes are offering the same route, then what will be the basis of selecting the best route?
2. Which of the processes will exchange the resulting LSAs with other OSPF neighbors?
Correct, different processes populate the same routing table when they are running in the same context. A common scenario for that is an OSPF-to-OSPF redistrubution: OSPF Redistribution Among Different OSPF Processes. This documet explains that the OSPF path selection rules do not apply among processes and what you need to do to avoid problems caused by that.
Another interesting link: Inter-Process OSPF Route Selection Rules and a recent discussion about path selection when ADs match: https://supportforums.cisco.com/message/4067146
HTH
Rolf
