Dog-eared means that a corner got folded down (making a diagonal) on a page as a bookmark. A dog-eared book isn’t necessarily beat-up beyond the damage to the corners of pages. Catty-cornered or kitty-cornered is adjacent to something on the diagonal, i.e. not orthogonally next to it like up, down, left, or right. So there is an argument to be made for a loose (coincidental) connection between those ideas, but I don’t think they come from the same roots.
The “E” (and similarly the “IE”) at the end is a very different pronunciation indicator than an “E” in the middle of the word.
There’s no need for the weird hate in your spoiler tag just because you don’t understand something.