That makes no sense. Just the brutal math of a polynomial is always going to be poor enough to notice than subpolynomial times.

Often but not always. Cool trick: any bounded limit is always O(1)!

Pick a small enough bound and an O(n^2) algorithm behaves better than an O(n log n). This is why insertion sort is used for sorting lengths less than ~64, for example.

Pick a small enough bound and certain O(n^2) algorithms will behave better than certain O(n log n) algorithms.

Big O notation doesn't take into account constant factors of overhead or plain old once-per-run overhead.

Sorry it was indeed a typo