3 octave range good for female singer 14 years?

In my opinion, there is no good and bad range. It is the quality and the work put into an instrument that matters. BUT having a 3 octave range is a plus for any age. If you continue to cultivate and take care of your voice from here on out, your voice could grow into something to reckon with as an adult. I have a pretty wide range, but I work on all facets of my voice to make myself accessible to different roles and solos. Since you have a decent range, you might want to invest in doing the same. You will love yourself for it in the end.

Yes, but expect it to get harder to have such a range. Your vocal cords are "loose" but have a hard time making the correct shape hence why it probably doesn't sound great and only good. Don't worry, keep at it and see you on american idol.