Omni-Changeling copies exactly what was printed on the original creature and nothing else, with the listed exception (unless that creature is copying something else or 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, or any non-copy effects that have changed its power, toughness, types, color, and so on.

If the copied creature is a token, Omni-Changeling copies the original characteristics of that token as stated by the effect that created that token, with the listed exception.

You can choose not to have Omni-Changeling enter as a copy of another creature. If you do, it will just be a 0/0 Shapeshifter with changeling, and unless another effect is increasing its toughness, it will be put into its owner's graveyard.

If the copied creature is copying something else, then Omni-Changeling enters as whatever that creature copied, with the listed exception.

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

Any "enters" abilities of the copied creature will trigger when Omni-Changeling enters. Any "as this creature enters" or "this creature enters with" abilities of the copied creature will also work.