When Zygon Infiltrator becomes a copy of a creature, it's neither entering nor leaving the battlefield. Any enters-the-battlefield or leaves-the-battlefield abilities won't trigger.

If it becomes a copy of a token creature, it copies the original characteristics of that token as defined by the effect that created the token. It won't become a token creature.

Zygon Infiltrator copies the printed values of the creature plus any copy effects that have been applied to it. It won't copy any other effects that have changed that creature's power, toughness, color, and so on. Zygon Infiltrator won't copy any counters on the creature, but it will retain any counters it already had on it.

If another creature becomes a copy of Zygon Infiltrator, it will become a copy of whatever Zygon Infiltrator is currently copying (if anything).