Rama,
I can provide high-level answers:
Yes, each system has a different visitor ID (this is not referring to the visitor ID service). The ID sync process creates a mapping as you have said on each system.
The reason is that each solution need to be able to work as standalone solutions and with other non-Adobe solutions.
Yes e.g. AMO's visitor ID syncing with AAM's visitor ID (called UUID).
This depends on the use-case and the destination. Most implementations will use automatic.
It is based on IDs, each system has their own ID structure and format.
E.g of mapping by ID sync, for user1: AMO ID: ABC == AAM ID: DEF
If the user1 is part of my shared segment to AMO, AAM could send AAM ID: DEF. AMO will look up previously ID sync'ed data. AMO will then know that user1 is its own AMO ID: ABC.
Yes.
AAM is DMP. Its main role is the segmentation in this use-case. AAM does not activate the segments.
In AMO, targeting audiences (AAM segments) is just one of many options to define the ad to be shown.
Please find a demo here: Global display ad campaign management | Adobe Media Optimizer