Re above...
#1 - For this reason, we make every effort to map all possible to Org-level Groups and avoid requiring any changes to Context Teams.
#2 - Agree
#3 - Query Builder Reports are the answer to this, and many, many other things. It's super laborious and error prone to one by one go to each context or each OIR, etc. in order to examine and possibly change it. We have gradually found ways to get Reports to show all this stuff over time. It's the only real way to have all in one place to examine. You still have to go to each context but at least you can see the results in one place. It seems fundamentally backward throughout Windchill that you can't at least that something exists from Site or Org in the Prod/Lib contexts.