Yes, different rooms. CC was demonstrating his latest weapon to potential clients, both parties had an interest in it.
Whether or not they would actually buy it, they at least wanted to have an idea of what it was.
The tea party may have been in a few days, but that doesn't mean they checked the loot given to them.
It's likely that they left it with Big Mom and then were dispatched to Punk Hazard to observe CC's weapon.
The races that live on Skypeia existed well before that segment of Jaya was blasted into the sky.
Only the Upper Yard region of Skypeia is from below the sky, hence the presence of dirt only there.
No, the film is not considered canon. Oda has confirmed this.
None of the Shichibukai had anything in particular to gain from going all out, Whitebeard died and Ace was executed.