Thespian's Stage

Thespian's Stage doesn't become untapped when it becomes a copy, even if the target land is untapped.

The copy effect created by the last activated ability doesn't have a duration. It will last until Thespian's Stage leaves the battlefield or another copy effect overwrites it. The permanent will no longer have the first ability of Thespian's Stage.

No enters-the-battlefield abilities of the land Thespian's Stage is copying will trigger. Thespian's Stage was already on the battlefield. Similarly, no "as this land enters the battlefield" or "this land enters the battlefield with" effects, such as that of Dark Depths, will apply.