i know there is a note after a hemidemisemiquaver, and it can be called a quasihemidemisemiquaver OR a semihemidemisemiquaver. which term is more correct? (i.e. which would you use in everyday life ?) i know they're rare, but still...

As you stated both are accepted. I prefer the use of semihemidemisemiquaver (I have also used demihemidemisemiquaver, it rolls better for me but is not acknowledged by any legit source as acceptable). I try to stay away from 'quasi' because I use quasi to mean similar to, or like something else. When I see it as a note description I don't think the accuracy of the note is as important, so I use the semihemidemisemiquaver.