I don't think so. When you know more and have more skills, your creativity is also boosted. Soma has lived all his life in Japan, so he would know nothing of great many things out there in the wide world. He might know some exotic (in Japan) things his dad tried back at the restaurant, but considering it was a place for affordable food, I doubt his dad used overly much imported stuff. However, go to India or Europe, and you would find everywhere stuff that would be rare in Japan (or vice versa). Soma is still highly lacking in that sense.
Not known by whom? The kids? I don't think the Nakiri geezer overruled Erina's decision to refuse Soma's admission into the school just to piss off his granddaughter. No matter what Soma's old man did in the past, for as long as Soma has been living (which is also about as long as the other students have lived) the man has mostly spent his time with Soma in the whatever town they were living in. I guess he would travel every now and then (don't remember if it was mentioned), but since he's now travelling, why not before? If he mainly travelled abroad to do some cooking, it's natural few of the students would know of him.