Does anybody know if the advantage cards in shadow of omega are discarded after use? All it says in the rules is a little mention of plot cards and sometimes they stay in play. Any answers would be helpful. Also the rules say to keep the mission a secret. How are you supposed to know if other players are playing the missions right? Maybe someone is cheating. Or maybe someone accidently skipped a part of their mission without knowing.

I'm 90% sure you discard. I just read it in my old rules version, I'll see if I can find it I the new rules.

You definitely discard an advantage card after using it, unless you use a character ability or such that allows you to put it back in your hand after use.

After a player completes the explore phase and chooses to do their mission, they flip over the mission card, thus revealing it. After completing the mission it stays out and shows the bonus they get for completing the mission. So, while they are completing it and afterwards, it will be right there for everyone to see if they did it right.