Except for the listed exception, Copycrook copies exactly what was printed on the original creature and nothing more (unless that creature is itself copying something 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 attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on.

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

If the chosen creature is copying something else (for example, if the chosen creature is a Clone), then your Copycrook enters the battlefield as whatever the chosen creature copied, with the listed exception.

If the chosen permanent is a token, Copycrook copies the original characteristics of that token as stated by the effect that put the token onto the battlefield, with the listed exception. Copycrook does not become a token.

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

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

You can choose not to copy anything. In that case, Copycrook simply enters the battlefield as a 0/0 creature and is probably put into your graveyard immediately, unless something else is increasing its toughness to keep it alive. It won't have "Whenever this creature attacks, it connives."

Once an ability that causes a creature to connive begins to resolve, no player may take any other actions until it's done. Notably, opponents can't try to remove the conniving creature after you discard a nonland card but before it receives a counter.

If no card is discarded, most likely because that player's hand is empty and an effect says they can't draw cards, the conniving creature does not receive a +1/+1 counter.

If a resolving spell or ability instructs a specific creature to connive but that creature has left the battlefield, the creature still connives. If you discard a nonland card this way, you won't put a +1/+1 counter on anything. Abilities that trigger "when [that creature] connives" will trigger.