2 - Real Answer: To preserve the surprise of his appearance in ESB
My "In-Universe" Answer: Due to his extreme old age, he has decided to remain in solitude, guiding other Jedi from afar through the Force, rather than participate in things that, despite his strength in the Force, might weaken or kill him from age.

5 - He sees Anakin as an incredibly useful tool, but if Anakin had any offspring, he may feel too attached to them and do what he does in ESB/ROTJ (try to have them help him overthrow the Emperor and become the ruler of the galaxy). Without them or the Jedi, Vader's on his own, with no one but Palpatine to be his "family."

6 - While the "Sith pirates" idea was interesting, since "Sith" is never mentioned in the OT, I don't think they need to be in the PT, either. I don't think the Jedi need to have an opposing Force-using organization. But I'm open to the concept if it can be done well.

7 - Because the Jedi Order for all intents and purposes no longer exists by the time of ANH (Obi-Wan and Yoda are the last).

8 - Because Bail Organa, her "father," was still alive and well on Alderaan at the time of its destruction, ruling as King - she would have taken over as Queen if he died (and Alderaan still existed).

9 - Luke/Leia's mother should raise her on Alderaan until her death early in Leia's life, while Obi-Wan could take the twins/Luke to Dagobah for advice from Yoda at the end of III about their/his fate (we see Obi-Wan land on Dagobah with Luke, but we don't see Yoda).

Those are my ideas, anyway - I don't really know about #s 1, 3, or 4.

I don't want you to post an outline if you feel it's not fleshed out enough, but I'd like to hear your concepts if you're willing to share.