I had forgotten that bit. Good catch. Since the Millennium Falcon isn’t that much larger than a fighter, and seems about as maneuverable as one, presumably it also slipped through the outer defenses.
Perhaps so, but Millennium Falcon engaged from above on Vader’s six. He wasn’t in the trenches, he would have been exposed to other AA batteries. So the theory holds that MF survived at least because it had deflectors, and likely because a lot of the other AA batteries likely had been disabled.
Perhaps so, but Luke’s wing were the only fighter craft left, and AA guns were still firing at them until they stopped firing to let Vader’s wing engage them. There demonstrably were AA guns still in operation when Solo swooped in - they were deliberately withholding their fire at that point.
It’s also possible, especially given the deliberately-World-War-II-era capacity of most sensors and data processing in the movie, that it was as simple as the gunners and lookouts being distracted and no one noticed a single small ship approaching to join the fray.
There’s also been a lot of fan speculation over the decades that Han Solo was unconsciously a powerful Force adept, who unknowingly Used the Force to pull off impossible maneuvers, perhaps such as slipping unnoticed and unscathed through the Death Star’s defenses.
Ultimately, of course, it’s because it was a suitably dramatic moment.
That’s not how the Force works!
Mostly true, though in addition to Luke and Wedge, there was also one Y-wing (pilot not established in canon, AFAIK) which survived the battle, as shown in this still of the ships flying away from the Death Star just before it explodes:
Ok, so that’s a point in @HMS_Irruncible’s favor. Maybe there was a wing of Y-Wings still taking out the surface defenses while the other fighters were making the trench run.
They usually store it next to the relative bearing grease. 
Well my broader point is that while AA was still active, there would be fewer due to combat damage. But now that I think of it, I only remember the fighters doing trench runs and dogfighting. And the operations briefing did not mention tasking anyone to suppress AA, so maybe there’s nothing to that line of thinking.
I think maybe because a bit of secrecy was required? I think pre-Rogue One the assumption was the Rebels didn’t want the Empire to even know they had the plans (lest they weld a two meter wide armored grate over the thermal exhaust port). The Death Star wasn’t exactly in the public domain at that point. hence the comment “that’s no moon, that’s a space station”, instead of “that’s the moon-sized space station that I just saw on the hyper-net blow the shit out of Jedha City and the planet Scarif after some sort of terrorist attack there.” In all fairness, they don’t really delve too deeply into how quickly news travels around the Galaxy in Star Wars.
At least you could still get an accurate weather report in some sectors.
I used to have that on a T-shirt, in fact. 