If the chord is C7b9 for instance, is it assumed that there you should also include a #9 and #11 in the chord. Maybe even a #13? Thanks for the help

A C7b9 chord is voiced C E G Bb Db. To maximize the tonal color, always place the Db at the highest note.
I like to use the 13 or b13 with the b9 to give it a more "open" sound. (C,E,Ab,Db)