Calix's last ability doesn't target any permanent. You choose which nonlegendary enchantment you control you're creating a token copy of, if any, as the ability resolves. No player may take any actions between your choice and the creation of the token.

Calix may be the target of its own constellation ability. This includes when Calix itself enters the battlefield.

If the copied permanent is a token, the token that's created copies the original characteristics of that token as stated by the effect that created that token.

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

Once you choose to create a token using the last ability, that ability won't trigger again that turn. Additional instances of the ability that are already on the stack will resolve but will have no effect.

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

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 copied permanent will also work.

The token copies exactly what was printed on the original permanent and nothing else (unless that permanent is copying something else or is a token; see below). It doesn't copy whether that permanent is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on.