Clarification on #1:
If you do not Kill Humbaba yourself, AND you have not received a notification in your team thread from one of the Game Administrators that Humbaba is dead, THEN Humbaba is still alive in your latest submitted game.
NOTE: Failure to acheive one victory condition counts as DEFEAT. That is non-negotiable. If you do not win the game, you are defeated. Even if you fulfilled 9 objectives, you will finish below any team that has won the game with zero objectives fulfilled, and not be eligible for awards.
Clarification on #9: Failure to fulfill a SECOND VC only means that you have not completed objective #9, but will still be in contention for Laurels and count as a victory.
None of the objectives are mandatory for your game to count as a victory. You may win by religious VC in the early BC years, and maybe you completed 4 objectives. If you think 4 objectives is enough to win laurels, you should be pretty happy.
If you instead believe that the best teams will complete all 10 objectives, then you should at least try to do so yourself -- in the fewest turns possible.
Clarification on #3) You ARE the UN sec gen or AP resident in your final submitted game. That's present tense, not ambiguous. Doesn't matter what happened before, I'll just look at the status in the final save. In other words: If a team lets the AP become obsolete and the UN is razed, this condition will be impossible to fulfill.
Clarification on #10) If you have submitted a victory or defeat or save with at least 100 turns played (or more) before the 2-month deadline, you have completed this objective and do not need to take any further action. If any objectives have become impossible to acheive in your turn 100 save, this information will be made public. But I doubt that will happen.