I don't have time to do any Operation "on time" do to me always being at work. Can they expire, then let me continue where I left off when I get the Operation reactivated again?
I'm not entirely sure myself but I do know that the operations you select and see on the first operations screen stay if you get new operations.
The thing is, I'm going for the Ghillie Suit. It may take me a month to do half a step. If the operations reset, then I won't even bother.
No, operations do not reset. You pick up where you left off when they become active again. Additionally, the operations that you are tracking on the main operations remain with you even after the others have changed.
They let you start where you left off. So if you got 22 dual wield kills towards akimo next time it is available it will start there.