To answer your questions:
Technically, no, but very often that's the assumption for guitar chords.
And doesn't suspended fourth mean that the fourth note is included and the third excluded? Usually, but music is about expression so the rules are routinely bent.
And isn't it the third note that determines whether a triad is major or minor? Yes, though it's clearer (!) to call the third an 'interval'; also see M. Ted's post.
How can you have a minor suspended fourth? See M. Ted's post.
Am I right in calculating that the addition of the sharped seventh is irrelevant to this dilemma? Yup. Unless you want another dilema - how to name the chord with a raised seventh instead of the 'dominant' seventh.
Is Paul Simon just playing with my head? Maybe.
...maybe there's a hidden message here for guitar players not to stress over their chords... Probably.
Back to Duckboots' daylilies.