Off the top of my head, I think something in traditional European beliefs said that the soul was at risk of flying out of the nose when one sneezed. Hence people would say "bless you" in case you died and were at risk of otherwise falling into hell.
"A sneeze is your soul trying to leave your body. Saying God Bless You shoves it back in."
I always say this as a joke. I'm pretty sure it's from the Simpsons, and not an actual historical belief. If you have any source that shows this an old wives tale or folkloric legend, I'd love to see it. That'd make it even funnier to me haha.
I was told this explanation in the 1970s by someone who was told it in the 1930s. So unless Groening is a time traveler, it didn’t originate with the Simpsons.
https://www.snopes.com/fact-check/bless-you/ is a good read; the truth is that Europeans and Middle Easterners have been doing it for so long (at least 2000 years) that the reason is lost to time; now it’s purely tradition/cultural. Early writings record that it was done, but not why.
Because the onus is on the farter to say something courteous. Because we, for some reason, decided that a involuntary, natural bodily function is rude.
I use it for all of those, but also if someone uses or words I don't understand or if they bite their tongue or anything similar. I successfully managed to confuse a lot of people doing that and it brings me great joy.
It's hard to say when it began, but it's a nearly worldwide tradition. Check out this page of different salutations: https://en.wikipedia.org/wiki/Response_to_sneezing
My belief is that it's generally because sneezing in a sign of illness, and illness tended to be more dangerous centuries ago, before antibiotics and when many people had less access to nutrition, consistent heating, sanitation and so forth.
It's because the demons fly out of you when you sneeze, and you need to be blessed to prevent them from getting back in, or so they thought back in Black Plague days.