"We are not children!"
Translation:Nie jesteśmy dziećmi!
The change to Genitive happens only when the positive sentence used Accusative. Which is a very big number of sentences already.
Because that's not a correct Polish sentence. It's totally ungrammatical. Looks like a direct calque from Russian.
Nope, because "jesteśmy" means "we are" and "mamy" is "we have". And "mamy nie dzieci" is ungrammatical by the way. If you want to translate "We have no children" it should be "(My) Nie mamy dzieci"
The most neutral negated sentence is when you put "nie" before the noun. Everything else puts strong emphasis on the word followed by "nie".
"It's not children who we are".
I don't even think this means that. "It's not children who we are" would rather be "Nie dziećmi jesteśmy", or preferably "To nie dziećmi jesteśmy" (this has the "It's" part).
"Jesteśmy nie dziećmi" is like writing "We are not-children" (plural of "a not-child")... plus making a mistake of writing 'nie' separately with a noun ;)