Bijuus are instantly aware, as seen with Bee. What does them having connected memories matter? Hinata was still awoken by Sakura.You are forgetting that both Naruto and Hinata were the only two people in the genjutsu that actually had their minds connected to view each other's memories. Not to mention the fact that Kurama has to actually be aware that Naruto was in the Genjutsu in the first place, and for all we know he could have been seeing the memories and probably shrugged it off. Even that is an assumption because Kurama himself did not even TRY to break him out, Sakura did.
Yes, because Kurama is going to leave Naruto there when he's on a mission to save someone,
There is no speculation here. Sakura breaks out first and then Shikamaru says that without her they wouldn't have gotten out.
Also, this has nothing to do with Nardo v Sauce.
Kurama isn't going to help anymore it seems.Yeah, if only he could break out of genjutsu without having Kurama.