Translation:Pigen har en grøn kjole.
Why not grønne?
"Grønne" would be for plural or if there is a definite article ("the"). Here, "dress" is indefinite singular, "a dress", so it takes the singular common form, "grøn".
why not "Pigen har grøn kjolen"?
That translates to "The girl has green the dress"
Doesn't make sense