Translation:My grandmother eats cake without sugar.
Should "My grandmother eats cake with no sugar" be accepted (English is my second language, maybe it is a hilly-billy talk, but I think I heard people talk that way)
Yes, that's acceptable. Another option: "My grandmother eats cake without/any sugar".
well... I assume an English person will say ”sugar free” also.... this sentence looks to me like in that old joke with the homosexual predator catching his victim and asking ”you have no way to escape, you can only chose if you want it with vaseline or without vaseline”, the victim thinks that it may be not so traumatizing if vaseline is used and says he prefers with vaseline, then the perpetrator turns around and screams in the dark ”hey vaseline, come here, we have a customer”...