I assume we are talking about a GUI software manager and not DNF.

I also assume that we want to deliver a user friendly package manager that is a pleasure to work with.

On that assumption:

Scenario 1: Blocking. You do not want to restart an application any time you want to start doing another operation with it.

Scenario 2: Not sure. If, in that situation, the application showed a message that freshly installed packages must settle first and that it needs restarting the application, I would think this is not blocking. Without explanation, this feels like blocking.

Scenario 3: Blocking if interactions like these are possible.

Scenario 4: Blocking. Dtto.

Scenario 5: Not blocking - a common bug candidate. This is a little wrongly implemented Scenario 6.

Scenario 6: Not blocking - actually this feels like a fair behaviour to me, although that train has gone and now we expect a little more.

Scenario 7: Blocking - clearly

If we just want to deliver a package manager that somehow "works" and do not bother about its user friendliness, then I switch Scenarios 3 and 4 to not blocking, but common bugs candidate.