No one really knows for sure. The closest Tolkien ever came to giving an explanation was a brief mention of how Bombadil was a manifestation of the spirit of nature and the surroundings of Tolkien's childhood home (or something like that, I'd have to look it up to find the exact quote).
That definitely is the best, and simplest, answer. No one knows
what he is, he just is.
Considering even Gandalf feared Sauron.. No. Gandalf was powerful, and they were both of the same stock of divine beings, but Sauron was, if he would have had the ring in his possession, far beyond even Gandalf in terms of power. Considering Sauron could most likely whoop the ass of a balrog if he wanted to, and even Gandalf feared the balrog of Moria, I think I can safely assure you that had Sauron gotten his hands on the One Ring, he could've mauled Gandalf with the flick of a thumb.
Haradrim or Southrons if you like.
This. If they actually tried flying into Mordor, Sauron would've noticed it immediately, and thrown everything he could of nazguls, fell beasts, black magic and whatnot at them. And even though Gandalf was a powerful divine being, he wasn't the Superman of Middle-earth, as he was definitely not invincible.
And now, the best theory regarding Bombadil:
Tom Bombadil and the Witch King are one and the same :lol