Dack's Duplicate

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

The +1/+1 counter is put on the creature before blockers are declared.

The ability of Dack's Duplicate doesn't target the creature.

Once dethrone triggers, it doesn't matter what happens to the players' life totals before the ability resolves. You'll put a +1/+1 counter on the creature even if the defending player doesn't have the most life as the ability resolves.

In a Two-Headed Giant game, dethrone will trigger if the creature attacks either player on the team with the most life or tied for the most life.

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

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

Any enters-the-battlefield abilities of the copied creature will trigger when Dack's Duplicate 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 the copied creature has {X} in its mana cost (such as Grenzo, Dungeon Warden), X is considered to be 0.

If the chosen creature is copying something else (for example, if the chosen creature is another Dack's Duplicate), then Dack's Duplicate enters the battlefield as whatever the chosen creature is copying. It will have haste and dethrone.