After selecting agents the clear buttons do dissapear. Another bug is that the same mission is already running so a duplicated mission should not appear at all. After starting the second one it does disappear. Same bug than in the last halloween event.
No they appear simultaneously, ie a second version of the quest becomes available on rotation while one is already in progress
This issue gets brought up every holiday with each new set of holiday overseer quests. The work-around to avoid it is, don't try to start the same quest that you already have running until after you've completed it. It would be nice though if overseer would pop up an error message if you try to start a new overseer quest that is a duplicate of one that's already running, or otherwise simply prevent it, instead of letting you try to start a dupe quest and then the display bugs out.