^^^ Edit: Nothing ulterior about it. It was implied before negotiations even began. Where else would Kojima even go? Nintendo? Sony can help him accomplish a lot more of his dreams gaming and otherwise than Nintendo are positioned to do.
I think this is largely a "Welcome to the family; get to know all your cousins" tour. KojiPro is independent, but during the announcement video, House made a point of welcoming him to the PlayStation family, which isn't a term they use for casual partnerships. Sony have had a pretty solid relationship with Kojima over the years, but that's been impeded by his allegiance to Konami. Now that he's his own man, then much like his guide, Cerny, he's now free to form any sort of relationship he chooses.
And I do think this is primarily a fact-finding mission for KojiPro. JJ may be an old buddy, but Kojima is definitely there to get input and feedback on his new studio, even if it's just advisory. Kojima's first project will be a PS4 game, but he has big plans for KojiPro, that may or may not involve JJ and Sony down the road. If Kojima wants to produce a movie based on his new IP, perhaps his buddy JJ will direct it for him, and his friends at Sony Pictures will help with distribution.
Yup, this too. Again, much like Cerny, now that Kojima is independent, Sony can let him very close to what they're doing if they choose to. I predict KojiPro and SCE will work very closely together in the future, and with Sony as a whole. Sony really are everywhere Kojima wants to be, so it seems like everybody wins here.
Very much like that, yes.