Muster the Departed doesn't need to have been on the battlefield when the creature died. For example, if a creature dies during combat on your turn and you cast Muster the Departed during your second main phase, its last ability will trigger at the beginning of your end step.

Muster the Departed's last ability will trigger only once during your end step, no matter how many creatures died under your control this turn. However, if no creatures have died under your control so far this turn as your end step begins, the ability won't trigger at all. It's not possible to cause a creature to die under your control during the end step in time to have the ability trigger.

If you control no creature tokens when you populate, nothing will happen.

The new creature token copies the characteristics of the original token as stated by the effect that created the original token.

The new token doesn't copy whether the original token 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, color, and so on.

Any "as [this creature] enters the battlefield" or "[this creature] enters the battlefield with" abilities of the new token will work.