1.) Well, you can't tell if their singing out of tune. If you've never heard the song, how could you possibly compare it pitch wise? It could sound completely out of tune and strange to our ears, but it could very well be what the original song sounds likes. We could assume that it could be out of tune, but we'd never be certain unless we heard the original.
2.)It really depends.
The key of a cover will depend on whatever the covering artist wants, but the spacing between each note is still equal to the spacing of the notes in the original key of the song in order for it to be in tune. So while it's different notes, the relations between those notes are the same. So it's not out of tune (provided that the instruments are also playing in the same key, or it's just the singer by themselves).
But say you there were a group of you singing the same song. Even if the relative spacing between notes are correct, if you're singing in a different key from everyone else, it's going to be out of tune.
I hope any of that made sense.
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