"I have a sister."

Both mean "a" or "an" but "un" usually goes with masculine nouns and "una" with feminine: un hermano, una hermana; un amigo, una amiga; un carro, una casa, un tío, una tía.

Yes you could . Yo tengo gives more emphasis .

I put tengo una hermana for I have a sister and was marked incorrect

Tengo - I have tiene - has