MTG Salvation

If I cast Flickerwisp targetting Awoken Horror, does it re-enter as a Thing in the Ice, and does it have 4 counters.

Sub-question, if it's not flipped, and I flicker it, does it have 4 counters.

Any time something changes zones (like being exiled and then returned to the battlefield), it is treated as a new object with no memory of its previous existence. So in both of your examples, it will enter as Thing in the Ice with four counters.