When flour gets wet, it sticks together to form dough. Dough can have large air pockets in it. Dry flour with a bit of humidity can also form these air pockets, albeit typically on a much smaller scale.

Whether you pack flour down or sift it through a sieve into your measuring cup can make a huge difference in the weight.

No, not at all. Volume ≠ Weight.

Another example: Some books use paper with bigger volume (so it looks thicker) but of course they are not twice as heavy suddenly.