Hshen -
Difference between AD permission and Mailbox permission is where the permission is stored (and, indirectly, on what object you're setting the permission). AD permission cmdlet sets permissions on AD objects. Mailbox permission cmdlet sets permissions on "store mailbox" objects inside the information store. There's a bit of overlap, however, because some of the permissions are AD permissions until the StoreMailbox object is provisioned in the information store, at which point they become read-only in the AD and are managed from the store object at that point forward.
As for extended vs regular rights in AD - the easy way to think of this is that generally the extended rights are the special things that are unique to an object (and are added for that object as part of its schema). So things that are particular to mailbox objects are going to be extended rights, while the common AD permissions for the mailbox object will be regular rights.
I believe you can still set ReceiveAs at the store object like you could in E2k3 to grant rights to all mailboxes in that store. I've not confirmed this, so please correct me (anyone) if this is no longer the case.
You can manage the output formatting of anything in EMS very effectively. The easiest way is to override the default "table" formatting that is causing this truncation with a "list" formatting that will show the whole property with a line wrap. Just "pipe" the output to "format-list" (or "fl") like "Get-AdPermission ADobject | fl" and you'll get a more verbose output that won't truncate.