I'm not sure if Sony owned a share in Square back then. While the Saturn was more popular in Japan at the time of FF7's release, it was possible that Sega wasn't planning on releasing it outside of Japan until they saw how it did first (maybe Sega was on a decline with the whole Sega CD/32X stuff not being too hot). Someone said that Square just moved into a new HQ, so maybe they didn't have enough money to publish the game outside of Japan, which prompted Sony to step in and offer Square they would publish it outside of Japan?
As for Extraction, I don't believe it sold too well on the Wii and maybe they wanted to recuperate some sales by porting it to the PS3, since the Move makes sense with that game. Why did they include it for free with retail copies? Maybe Sony offered some incentive (cheaper costs for licensing) for EA, with whom they already have a good relationship. Extraction is on sale on PSN for $15 anyways, although EA didn't do the same thing with Medal of Honor: Frontline (free with every copy of MoH).
LA Noire has been talked about and Netherrealm Studios has mentioned they wanted a 360 exclusive character for Mortal Kombat, but something happened that made them forget that.
