This effect has no duration. If you use the ability, Cemetery Puca will remain a copy of the creature until it leaves the battlefield or you use the ability again. If it becomes a copy of a different creature card, the new copy will overwrite the old copy.

Cemetery Puca copies the printed values of the creature, plus any copy effects that have been applied to it. It won't copy other effects that have changed the creature's power, toughness, types, color, or so on. It also won't copy counters on the creature (it'll just retain the counters it already has).

If Cemetery Puca becomes a copy of a token, it copies the original characteristics of that token as stated by the effect that put it onto the battlefield. It does not become a token.

Cemetery Puca's ability isn't targeted. It can copy a creature with shroud or protection.

If multiple creatures are put into their owners' graveyards at the same time, Cemetery Puca's ability will trigger once for each of those creatures. You choose the order that those abilities will resolve. It's possible to pay , have Cemetery Puca become a copy of something, activate an activated ability of that creature, then pay again, for example. It will end up a copy of the last creature card paid for.