One doesn’t have to be an atheist or agnostic to be a secular humanist. The other option would be apatheist (which is not necessarily atheist, as I’ll get to later.)
Apatheism makes the most sense to me as a term regarding ethics: what’s right vs wrong, and how should I behave, rather than metaphysics, which is about “what is”. But it can apply both ways. In the latter sense, an event like this would lead to an “oops” moment.
Ethical apatheism can apply regardless of one’s belief in whether gods exist. In “The Flies” Sartre covers the case of apatheism in the context of an extant God. Orestes chooses an ethic that defies Zeus. It’s a great play and a quick read.
Metaphysical apatheism could be rendered null given proof that gods exist. Of course, this could just be proof that superior beings exist, in which case the argument changes from whether they exist to whether they’re gods or not, and the apatheist can still say “I don’t care”.
Perhaps because you’re being polite. It’s considered impolite to challenge someone’s religious beliefs, but this injunction doesn’t necessarily apply to issues with less emotional intensity.
However, the emotional intensity does seem to apply to homeopathics, so perhaps it’s really pretty much a religion, and you might want to rethink. I find that reactions to arguments of science and logic on homeopathy are pretty much the same as for the same on religion. 
No, the apatheist’s position is that it hasn’t happened and he isn’t going to worry about it happening, and (in the case of ethical apatheism) even if it does, it doesn’t affect his judgement of right and wrong.
I first saw the term in “Puddnhead Wilson”. Since then I’ve read all of Twain’s novels (gotta love cheap classics on ereaders!) and he uses it in a few others. I get the sense that it was common usage at the time. I also get the sense that Twain considered himself a free thinker.