Kaya, ungreifbare Jägerin

Any enters-the-battlefield abilities of the copied permanent will trigger when the token enters the battlefield. Any "as [this permanent] enters the battlefield" or "[this permanent] enters the battlefield with" abilities of the chosen permanent will also work.

Except for the listed exceptions, the token copies exactly what was printed on the original permanent and nothing else (unless that permanent is copying something else or it is a token; see below). It doesn't copy whether that creature is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, and so on.

For the middle loyalty ability, each opponent in turn order chooses whether or not to scry. Those who do (likely all of them) look at the top card of their library at the same time, then they decide in turn order where their card goes. Each opponent will know the choices of previous players in turn order before making their own choices.

If the copied creature has {X} in its mana cost, X is 0.

If the copied creature is a token, the new token that's created copies the original characteristics of that token as stated by the effect that created that token, with the exceptions noted above.

If the copied permanent is copying something else, then the token enters the battlefield as whatever that permanent copied, with the exceptions noted above.

Kaya's last ability checks to see whether the permanent was an Aura when it last existed on the battlefield, not whether it is an Aura card in exile. For example, if an enchantment creature with the bestow ability (an ability that allows a creature card to be cast as an Aura instead) is an Aura and the target of Kaya's last ability, the ability will not create a copy of it.