1) Speculating on how Soifon's bankai could be better is fanwank territory. The fault for Soifon's stupid banki dons't rest in Yoruichi's not taking her, but in Kubo's inability to do things that make sense anymore. But more importantly; Yoruichi taking Soifon with her wouldn't change her core personality, which is what her banki is based on.
Their relationship would probably be worse than it was before they left, in my opinion. Free from the duties of the Onmitsukido, Soifon could dedicate even more time to Yoruichi. Never separating form Yoruichi would stunt her personal growth even more than it already was.
I can't comment on the fate of the Onmitsukido.
2) I think Yoruichi would regret not saving Urahara, Tessai, and the Vizards. Aside from the fact that they were the only ones who new what Aizen was really up to, I don't think her conscious could take it.
I'm all on board the guilt train as to why Yoruichi saved everyone back in the day. Her self-imposed exile was her own way of atoning for her court-marshal worthy dereliction of duty.
I really can't say how she would handle Aizen in this senario. I don't think she would tell Soifon anything. If Soifon knows, she will get involved, and that would put her in grave danger. Yoruichi already ruined eleven lives, so I don't think she would want to make it twelve.
Ultimately, Yoruichi is damned if she did and damned if she didn't.
3) Prepare your pitchforks, but I don't think either of their lives would be that different if the other never existed.
Both of their fates were decided form birth. If Soifon never existed, she still would have been the head of Onmitsukido and the Second and friends with Urahara, who would create the hogyoku that would result in all the problems in Bleach.
Soifon would be indoctrinated to worship whoever was the head of the Shihoin house, so she's doomed no matter what.
4) I don't think Soifon would take Yoruichi under her wing and make her a confidant. She's concerned with protocol. She would insist on the proper title's and procedure. She would keep Yoruichi beyond an arms length.
5) Soifon would get involved, and probably get herself killed.
6) I don't think she does. Her emotional instability shown during her fight with Yoruichi is the result of her trying to reconcile her conflicting emotions; the fantasy of Yoruichi that was instilled in her from birth and the reality of the woman.
I don't think Soifon knows who Yoruichi is, so she can't possibly know how she actually feels about her.