When someone sneezes, should I say something? (Like bless you in English)
--> Saying nothing has no problem in Japan. Or we ask someone who sneezed だいじょうぶですか(fomal)/だいじょうぶ?(informal, between close people). The subtitles often say おだいじに, however, I rarely say it to someone who sneezed.
I hope this was helpful.