1. Eldar codex psychic powers have their own rules covered in the codex, one being not requiring line of sight for some. Ones that require a target still need LOS just like a shooting attack.
Yes, and specificaly in the case of Eldar psychic powers this means that
a.) Destructor, Eldritch Storm and Mind war are
psychic shooting attacks and need LOS.
b.) Fortune, Guide and Doom can be used as stated in their codex description (for now).
2. Disembarking does not remove the effects of crew shaken or stunned from the models that were embarked. So passengers that are "crew stunned" can not fire in their next shooting phase regardless of disembarking or not. This does however not stop them from using psychic power only PSAs.
Exactly what I wrote.
And if you come to think about it, non-PSA
powers would still be used at the beginning of the movement phase, and thus before the disembarktion, so they would be covered under question 1 again.