The rich and powerful take what they want. We steal it back for you.
Where to deploy from if there is more than one Islamist Rule country (random?)
The Deploy From column on the Priorities Table will determine this. If you still have multiple choices here, then random roll.
Third box: Does that mean Good (any alignment) then Fair Ally, or
Good Ally then Fair Ally?
I'm assuming Good Governance then any Fair Ally, but this is a question better answered by Adam.
Again I assume if there is more than one country meeting these criteria, choose at random..?
Yes, provided you went through the Priorities Table as well.
the without cells OR with Troops test implies deployment from a country without troops. How is that possible?
It's not. The bot wants Troop cubes that are in a country without any Cells present or with a Troop marker (since they don't Deploy these) or Militia present.