Learn French: C'est une fille. Elle est très jeune. - She is a girl. She is very young.

This is the core rule of your current lesson! In French, you use C'est to identify what someone is by using a noun (here, une fille). You switch to Elle est (or Il est for males) when you are simply describing them with an adjective (here, très jeune).

Could I just say Elle est une fille?

No, that sounds unnatural to a French speaker. Whenever a noun has an article in front of it (like un, une, le, or la), you must use C'est instead of Il est or Elle est.

Jeune describes a girl here. Does it need an extra 'e' added to the end to make it feminine?

No, jeune is spelled exactly the same way for both masculine and feminine words. When a French adjective already ends in an unaccented e in its base masculine form, you do not add another one.

Since C'est literally means "It is", could C'est une fille also mean "It's a girl"?