If the meat was rotten, could the steam potentially carry bacteria from the still-raw meat when you start to cook it, and could the steam carry that up to your nose and get bacteria in your nose or eyes?

l have never heard of that - but if it smells that bad - toss it in the trash right away.

My dad used to cook burger meat and bacon for himself that to me smelled past its prime and it never seemed to hurt him.go figure.

the heat typically kills the germs, but if the meat was rotten or smells bad(unusual) while raw, l personally would just throw it out.

NO. Infection requires direct contact.

Wow, bacteria and steam don’t get along.