In some instances, using "got" is not good English, in others it is, more for the sake of euphonics than meaning or rules of grammar. "I've no stone" or "I've got no stone" - the latter sounds more complete in it's meaning, the former somehow incomplete, like it's missing a word.
Also "got" is usually used in good English as an emphatic. "I've got no stone!" "I haven't got a clue!". Used when emphasis is not intended or perhaps not wanted, then it's just not good English. "I have no stone" is not the same as "I have got no stone" because the latter is more emphatic.
Certain nouns in Russian have what's called a "fleeting vowel," always an "e" or "o." They're there when there is no ending, such as камень. When an ending is added, in this case the genitive я, they go away again, so камня. The opposite can also happen, which was explained in a previous lesson. Some do not have it in their nominative form, such as девочка, but when the "a" ending disappears, a fleeting vowel shows up: девочек. The point of them is simply pronunciation. You can't pronounce камнь or девочк, or not easily, so a vowel comes in to help. When it's no longer necessary for pronunciation, it goes away again.
I'm coming to the conclusion that Duo's approach to Russian is poor, because of the multiplicity of endings which change according to case - and the spelling rules. This kind of grammar requires lots of drilling, to see how endings change as one moves from case to case. Jumping around with haphazard selections of gender and sometimes number fails to give a foundation to understanding how case operates to change endings.
My conclusion is based on the certain knowledge that repetition is one of the most important keys to learning grammar, and with case-significant languages, drilling on different words with the same gender and number, moving from nominative to genitive, nominative to accusative, prepositional - would be a far better way of teaching the case system of Russian.
I'm really considering dropping the Russian course and finding a different course somewhere else because learning the cases is so frustrating here.