I don't know where did you draw that conclusion from but the Kid pirates were never a "parallel" to the SHs. Just a rival pirate crew.
I don't remember him saying that, but Laws plan was to form an alliance with the SHs (which he did) to kill Kaido (current events). Whatever he did or didn't say must've been out of despair because of his history in Dressrosa with Corazon and Doflamingo. Law met Bepo, Schachi and Penguin when they were young. He's not severing that bond to join the SHs. You're fanboy of Law, but you underestimate him. Law isn't low and selfish to abandon his 3 friends (and the rest of his crew) and he doesn't act on emotions (maybe in certain situations) but he thinks logically and plans ahead. Law would be an ally to the SHs rather than leaving his crew to disband. He will either find out about the will of D as an ally of the SHs or find someone else like Robin who knows about history.
Yes!
Also if anyone joins the SHs after Yamato, that would be Bon-chan. Bon-chan for Nakama. Jinbei, Hancock and Law did help and save Luffys in certain situations, but Bon-chan was the star of Impel Down, he sacrificed himself to save JoyBoys life.
Bon-chan fulfils the role of a Spy, he plays it better than Kanjuro thanks to his DF. So he'd be a great infiltrator and a combatant.