“Entendre” in this sense doesn't really mean “know”, it means “understand”. That sentence means “I don't understand the first thing about fashion”, not “I don't know the first thing about fashion”. Granted, the meaning is almost the same, but not exactly the same. But “je ne comprends rien à la mode” suggests that the speaker doesn't understand what makes people interested in fashion or what can make things fashionable, whereas “je ne connais rien à la mode” just says that the speaker is aware that this is a topic that some people know better than others, and that the speaker knows less than anybody else.
Entendre in the sense of “understand” is very old-fashioned. It isn't really used anymore. It was still common in the late 19th century, but fell into disuse in the early 20th. As usual, it survives in a few expressions, such as “laisser entendre” (which means “let believe”, constructed as “cause to understand”, and definitely not related to hearing). Back when entendre meant “understand”, the word for “hear” was ouïr, which is not really used anymore.
“Je ne connais rien à la mode”, “je ne connais rien au vin” are perfectly ordinary, idiomatic French sentences. “Je ne comprends rien à la mode, au vin” are also idiomatic, with the nuance to the meaning that I explained above. Using “entendre” sounds weird out of context and implies “this is the 19th century or earlier”.
The preposition en doesn't work and I have a hard time explaining why. “Je connais quelque chose à la mode” is fine, but “*
je connais quelque chose en mode” and “* je ne connais rien en mode” are not. On the other hand, you can say “je m'y connais en mode” or “je ne m'y connais pas [du tout] en mode”, it's informal but idiomatic.