There are multiple Persona 3 movies. =)
Sure, but it should be expected that this will be game related given the logo on the website.
I'd be fine with this even if it's just P4A2 related, but it's probably more than that.
In regards to which platform Persona 5 could be on, keep in mind Atlus are listed on the Sony 3rd Party Team which does imply something.
It implies Daylight.