Re: Why didn't Picard know Sito Jaxa ['Lower Decks'] was on his ship?
He knew, he wanted her on the ship.
Furthermore, he mislead her as part of the overall test of her character for the mission.
The use of her in that episode was very, very well done. Lower Decks is one of TNG's better episodes. (Though one wonders how she graduated and got a commission on the Enterprise before Wesley did.
For me, and for many of us, the future is now in the past.