1. when do we upgrade to another ship?
2. I'm trying to find some Generators for a planet in the sector left to the orion, I have no clue where to find them, the description from the message and the quest journal don't really help me much any clue where to find them or point me in the right direction...
As far as I recall you don't need to do any mission to unlock Klingon. Just reach level 6 and it should unlock for you at character creation. Unless I'm missing something... I don't ever recall doing a mission to unlock the Klingon side.
Do you "have" to take the mission at Level 6 (IIRC) that also unlocks Kilngons if you have no plan on ever playing a Kilingon?
I think you may have to take it if you want the storyline to progress (never actually tried not taking it myself), but there's nothing forcing you to make a Klingon character if you do, so you should do it just to get the points to spend on your character and bridge officers.