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If the token isn't exiled at the beginning of the next end step (perhaps because the delayed triggered ability is countered), it remains on the battlefield indefinitely. It continues to have haste.
If the copied creature is copying something else when the ability resolves, then the token enters the battlefield as a copy of whatever that creature is copying.
Any enters-the-battlefield abilities of the copied creature will trigger when the token enters the battlefield. Any “as [this permanent] enters the battlefield” or “[this permanent] enters the battlefield with” abilities of the copied creature will also work.
The token is exiled at the beginning of the next end step regardless of who controls it at that time.
The token copies exactly what's printed on the original creature and nothing else (unless that creature is copying something else; 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.
If another creature becomes or enters the battlefield as a copy of the token, that creature won't have haste and it won't be exiled.
If the copied creature has in its mana cost, X is 0.
If the ability resolves during a turn's end step, the token will be exiled at the beginning of the next turn's end step.
