Dämmerungsdeuterin

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

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

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

The token created by Twilight Diviner's last ability copies exactly what was printed on the original permanent and nothing else (unless that permanent is copying something else; 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.