They're both grammatically correct (there's just a spelling mistake in 'photogrEpher'). There could be a slight difference in meaning in that the first sentence makes it clear that she's talented when it comes to music but perhaps she's not that great as a photographer. But then again, the same could be inferred from the second sentence, so I'd say both mean pretty much the same. Hope it helps!

The 2nd sentence is concise and maintains a parallel formulation of clauses.

They are fine. There's no real difference. You could just go for "She is a talented musician and photographer", unless you want to leave open the meaning that she is talented in music, but not in photography. Sara's right about the spelling typo, obviously.