Translation:A plane was flying in the sky.
it's more to do with the distinction between てある and ている. てある denotes an action that has occurred and been left that way (ie まどは閉めてある). it's like saying "the state is that the window is shut. ている gives the impression that it is in the process of occurring, known as the continuous aspect (not to be confused with continuative form/連用形)
Yes, because into designates a direction, as if it were taking off from the ground into the sky, and for that we would need に or へ instead of を. The sentence is describing where the plane was flying.
"Flew" is also the wrong word here, as this sentence is in the past-progressive, and "flew" is the simple past. For reference, that would be 飛びました.