I think they are all OK and have the same meaning but (b) and (c) sound the least natural.
Also it's not clear that the noise is coming from the eating when you say it like this. (Maybe you are making noise by tapping your foot.) To be perfectly clear it would be better to use an adverb like noisily. Or to say what kind of noise it is.
e.g.
Eating noodles noisily is not bad manners in Japan.
Slurping when eating noodles is not bad manners in Japan.