1. The best science advisor by far is Stoyan from the Draug system, with a massive 75 skill points in science. He's an elector who starts off with a neutral opinion of Zorana, and but his favor can be lost pretty quickly, since he has a LOT of enemies. But his 75 points are so good that I can't bring myself to care. I've even had him try and assassinate me as a member of my cabinet. Just a part of his charm.
Another good choice for science advisor is Lorkas from Tharkas II, who has a respectable 60 points in science.
2. Good etiquette and first impressions do always help - but I don't think the benefits are strong enough that I'd be burning away turns in deep space. Not unless I was trying to poach one of the Myrkka I electors before Lukomir swoops in, and I was working towards a very particular set of skills.
As for 3, 4, and 5, they all have the same answer: no, not that I'm aware of.