Scans often arrive with a broad white border, and academic papers give up a surprising amount of every page to margins. Both are easy to trim back.
Every PDF page carries a box that tells a reader which part of it to display and print. Cropping moves that box inward. The content outside it is still in the file, it is simply no longer shown.
The good consequence is that this is reversible and adds nothing to the file size, so an aggressive crop costs you nothing and can be undone later. The important one is that it is not a way to remove something sensitive from the edge of a page, because the content remains in the file for anyone who looks properly.
If a scan is skewed rather than merely wide, crop after straightening, not before. Cropping a tilted page to a tight margin clips the corner of the text on the side it leans towards.
No. It changes what is shown, not what is stored, so the size stays about the same.
Yes. Set the trim, name those pages, and save. Run it again with other settings for a different set.
No, and you should not try. The content is still in the file. To remove it properly, export the pages as images.