If the question is complete level 1 GE and you’ve completed that already, yes the quest will then be automatically completed.
^ Correct. If a quest asks for something that you have already done, it will auto-complete.
For example, completing level 1 of GE, acquiring a specific province, have X amount of a specific building in your city
(not "build", different wording you see), etc which were already completed before getting the mission, will auto-complete.
If you believe there's an issue with a quest, however, always feel free to contact support to look into it further for you, we're always happy to help.