Pirated Copy copies exactly what was printed on the original creature and nothing more (unless that creature is copying something else or is a token; see below), except it will also be a Pirate and have the granted ability. It doesn't copy whether that creature is tapped or untapped, whether it has any counters on it or Auras attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on.

Being a Pirate and having the granted ability are part of the copiable values of Pirated Copy. If another creature enters the battlefield as or becomes a copy of Pirated Copy, it will copy whatever Pirated Copy is copying, be a Pirate in addition to its other types, and have "Whenever this creature or another creature with the same name deals combat damage to a player, you draw a card."

If Pirated Copy doesn't enter the battlefield as a creature (such as by copying an artifact or land that became a creature), it doesn't become a Pirate, though it still has the granted triggered ability. It won't become a Pirate even if it later turns into a creature from another effect.

Pirated Copy's ability doesn't target the creature.

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

If the chosen creature is copying something else, then Pirated Copy enters the battlefield as whatever the chosen creature is copying. It will also be a Pirate and have the granted ability.

If the chosen creature is a token, Pirated Copy copies the original characteristics of that token as stated by the effect that put the token onto the battlefield. Pirated Copy is not a token, even when copying one.

Any enters-the-battlefield abilities of the copied creature will trigger when Pirated Copy 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 Pirated Copy somehow enters the battlefield at the same time as another creature, Pirated Copy can't become a copy of that creature. You may choose only a creature that's already on the battlefield.

You can choose to not copy anything. In that case, Pirated Copy enters the battlefield as a 0/0 Shapeshifter Pirate creature, and will probably die almost immediately, when state-based actions are next performed.