Silent Hallcreeper copies exactly what was printed on the target creature and nothing else (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.

The phrase "that hasn't been chosen" refers only to that specific Silent Hallcreeper. If Silent Hallcreeper leaves the battlefield and then returns to the battlefield later, it will be a new object with no memory of the modes that were chosen when it was last on the battlefield.

If the copied creature is a token, Silent Hallcreeper copies the original characteristics of that token as stated by the effect that created that token.

When Silent Hallcreeper becomes a copy of the target creature, it's neither entering nor leaving the battlefield. Any enters-the-battlefield or leaves-the-battlefield abilities won't trigger.

If the third mode is chosen for Silent Hallcreeper's last ability but the target creature is an illegal target as the ability tries to resolve, it won't resolve and none of its effects will happen.

While Silent Hallcreeper is a copy of another creature, it won't have any of its previous abilities.

If the copied creature is copying something else, then Silent Hallcreeper becomes a copy of whatever that creature copied.