I have a problem understanding the need for the word “no” in sentences like : I don’t eat no meat. - I don’t smell no dinner cooking. ... Why would we need to add “no” if we already have “Don’t” in these sentences ? Is it grammatically correct ?
You absolutely don't need "no" in those sentences, and those who believe that there is only one "correct" English will say that you mustn't use "no".
Millions of English speakers in many parts of the world customarily use "no" in sentences like those. In many other languages this sort of construction is normal; but a couple of centuries ago some writers made up rules for English that said you mustn't, and somehow persuaded other people to believe them.