You choose whether to pay for Emiel's triggered ability while it's resolving. If you do, no player may take other actions between the time you pay and the time the creature has one or two +1/+1 counters on it.

When the card returns to the battlefield, it will be a new object with no connection to the card that was exiled. Auras attached to the exiled creature will be put into their owners' graveyards. Any Equipment will become unattached and remain on the battlefield. Any counters on the exiled creature will cease to exist.

If the entering creature is a Unicorn, you still have to pay to put two +1/+1 counters on it.

Emiel's second ability triggers whenever any creature other than itself enters the battlefield under your control, including those returned by its first ability.

While resolving Emiel's triggered ability, you can't pay more than once to put more counters on the creature.

If a token is exiled this way, it will cease to exist and won't return to the battlefield.