Ace of sky, ace of skies, ace of the sky, which one is correct? I've googled it and apart from some games, there isn't much of that expression. Is it common (at all) or is it common just for combat pilots? Could it be said in affectionate way to airline pilot (or any kind of pilot) especially if that person is someone close, e. g. husband, brother... ? Is there better expression for pilots? Thanks.
In general informal English, an "Ace" is someone who is highly skilled. You could talk casually about "an ace carpenter" or "an ace teacher". It comes from the term "Flying Ace" which specifically means a fighter pilot with (usually) five or more confirmed kills.
I've not heard "Ace of the skies" but I would assume you meant "flying ace" but you were translating the term incorrectly.
Spouses have all sorts of nicknames for each other. It is possible that a husband could call his pilot wife "ace" or vice versa, but it would not be technically correct nor would it be very common. Even actual Flying Aces are not usually called "Ace" as a name. Normally a husband or brother would call his wife/sister by her name, or a nickname (perhaps unrelated to flying).