Is it possible to copy a land with Mimic Vat that is turned into creature by an enchantment?
When a non-creature card such as a land is put into a graveyard from play and it is a creature when it dies, you can use Mimic Vat to exile it, and create tokens later.

When you do this, you will create tokens of the card that was exiled, Mountain, not the creature that it was when it died.

One of the rulings on the Gatherer page says:


  You may exile a noncreature card with Mimic Vat's first ability. For example, if a nontoken artifact that's become a creature is put into a graveyard from the battlefield, Mimic Vat's first ability triggers and you may exile that card.


With regards to whether the triggered ability will still trigger, even though Awaken the Ancient stops enchanting the Mountain when it dies, rule 603.6d says


  Leaves-the-battlefield abilities... will trigger based on their existence, and the appearance of objects, prior to the event rather than afterward.


This means that since the Mountain was still a creature before it left the battlefield (and caused the Aura to become unattached), it does trigger Mimic Vat.