Singing on key/in tune. Can anyone help?

Hey guys, I have two singing related questions. Firstly, I was
wondering, is singing a learned talent or a natural one? I've been
having lessons since January, and I think I have improved a whole lot
since then but I'm still nowhere near amazing. Do you have to be born
with the gift of singing to be up there with 'the best'? Secondly,
whenever I sing I sometimes find it hard to stay in key. I find it
easier/easy to stay in tune/key if I'm playing the piano or guitar.
However, when my voice teacher plays the piano I just seem to go off a
lot and it really frustrates me. (Sometimes I manage to stay
completely in tune, but not always). Is there anyway to sort this? Is
there any method/exercises to stay completely on key all the time?

Extra info : When my voice teachers plays scales and exercises, I
manage to sing them fine, when it comes to songs, I just go
off...thanks guys!