Madness type 3 is almost a useless ability given in order to shrug it off you just need to be exposed to creepy eldritch stuff. So Link being unfazed with stuff like Majora or Bongo Bongo qualifies him for that.
Fear is a subset of mind manipulation.
Already proved that the corruption is resisted several times, through natural resistances, the Master Sword's purging, and the Moon Pearl.
Reaching Mundus isn't hard given he's not omnipresent. Invisibility is outdone by the Lens of Truth if he has it. And you'd have a point with NEP if it were type 2.
I have the disease quote right here. Not only is Link not fighting in the demon world, but Dante was able to will himself into fighting condition and it took at least ten minutes going further into the demon world to start screwing with him.