Evil Twin copies exactly what was printed on the original creature (unless that creature is copying something else or is a token; see below) and it gains the activated ability. It doesn't copy whether that creature is tapped or untapped, whether it has any counters on it or any Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, or so on.

The activated ability that Evil Twin gains as part of its copy effect is a copiable value that other effects may copy.

If the chosen creature has in its mana cost, X is considered to be 0.

If the chosen creature is copying something else (for example, if the chosen creature is another Evil Twin), then your Evil Twin enters the battlefield as whatever the chosen creature copied.

If the chosen creature is a token, Evil Twin copies the original characteristics of that token as stated by the effect that created the token. Evil Twin is not a token in this case.

Unless a token is a copy of another creature or was explicitly given a name by the effect that created it, its name is the creature types it was given when it was created. For example, the Beast tokens created by Thragtusk and by Baloth Cage Trap are both named "Beast."

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

If Evil Twin somehow enters the battlefield at the same time as another creature, Evil Twin can't become a copy of that creature. You may only choose a creature that's already on the battlefield.

You can choose not to copy anything. In that case, Evil Twin enters the battlefield as a 0/0 creature, and is probably put into the graveyard immediately.