"She is a 15-year-old girl" is correct, because "15-year-old" is used as an adjective to describe "girl." For the second one: "gonna" is not a word!! You can't use it in writing. You can say: "My vacation is going to last for 10 days." "Are" is not correct in this case.

Thank you very much guys!

It's a word in spoken speech, but you can't use it in writing.

I would argue that gonna is actually a word, albeit a slang word. You would sound lazy or dumb using it in a formal setting, but amongst close friends you could use it. It is much like how people argue that "ain't" isn't a word and yet it appears in the dictionary with a usage note and you encounter it all the time in spoken informal settings. lol But my criteria for what makes something actually a word is whether it is in use by a sizable number of people and not what some grammatarian likes to impose on a language. hahaha :)