Yes. Schools absolutely need written parental consent for IQ testing and most individualized achievement testing (meaning testing that is specific to a particular child, and not administered school- or class-wide). And no, most don't notify about the exact date, mainly because one can't always predict when it will fit into the day, as the same people who test often do crisis intervention and counseling as well. Although if a parent writes a note in the section on the consent form that asks for input which suggests that the child will do better under some specific circumstances, I generally call home and ask for details, which sometimes results in making appointments.
Another big difference between private testing and public school testing is that most of the private testers I know do the testing in a single all-day session (your testers may have different practices), whereas most of the public school testers I know will spread out elementary-age testing over several days, with shorter (under an hour) sessions each time. (Again, your schools may differ.) I'm assuming this simply has to do with the greater access school testers have compared to private testers, which allows for stopping when/if the child is fatigued, and waiting for a better time. With adolescents, I have even negotiated with them to test during preferred times and dates. (Although there's always that one kid who wants to be pulled out every day during their least favorite class!)
And lack of sleep definitely affects IQ test results, especially in working memory and processing speed. Just as you would expect from personal experience.
