Unfortunately, it IS the full explanation. Like R.A.Barber said: look at the shadows of the building. Again with your latest example the shadowline connects exactly to the top-most corner.
What would you expect? Overhanging roofs, awnings etc will always, no matter how you correct the images, obfuscate the true outline at ground level. And it is that building outline at ground level which is part of the BAG. And no matter how you take your photographs: buildings (and especially taller buildings!) will always show parallax, which will be 0 in the dead center of the photo, and steadily grow bigger as you approach the edge of the photo. There is no way around that, it even happens in your own eyes. It’s because the rays of light all come in through the focal point - with the emphasis on point.
And then there is the fact that what you see on the aerial photograph is the roof structure, while in the BAG you’ll find the wall structure at ground level. So they are not even the same objects.
This is true, but it means something different than you think. It does NOT mean that all the parallax has been removed (that is impossible), it means that corrections have been made for the plane not flying absolutely horizontal while the photograph was taken. A plane will always be a little bit (or sometimes more, in case of turbulence) off a perfect level flight - and that is what is being corrected when you’re talking about ortho-rectified aerial photographs.
There isn’t. You’ll never get the aerial photographs to exactly fit the BAG geometry, if only for the reason that they show very different parts of the same object that aren’t even on the same altitude. Apart from the parallax which you will encounter in every single image.
I do not know what you mean by this, or what you want to achieve by it, but I think it would be a waste of time if you ask me. As I tried to explain: filtering on some criteria is not going to help you.
On the whole, if there is a specific reason that you were trying to achieve a perfect match between aerial photograph and BAG geometry, if you can explain what that is we might be able to figure out something - there are always more ways than one to achieve things in the geo-world