Lady Orc, glad you're trying this again.
First question, you only count 2 days. Keep in mind, though, that if you return at 1 am on the 3rd day, that counts as 3 days.
Second question, each step would be considered an opportunity, but you could do as much of the Morcu Corp adventure as you want, you just can count only 3 of them.
Third question, Private eye cases count as black ops. Supermaxing any of the instruments is next to impossible. You can try, but have a back up. My rock star never got any of the ten opportunities needed.
Hope this helps.