The enchanted Mountain retains any other types or subtypes it may have. You can still tap it to add . It can be affected by anything that affects either a land or a creature.

Copies of the enchanted Mountain won't be 7/7 red Giant creatures with haste. For example, if Awaken the Ancient is enchanting a basic Mountain, a copy of that creature would just be a basic Mountain.

If the enchanted Mountain stops being a Mountain for any reason, Awaken the Ancient will be put into its owner's graveyard as a state-based action.

This doesn't count as a creature entering the battlefield. The Mountain was already on the battlefield; it only changed types.

Awaken the Ancient can enchant any land with the subtype Mountain, not just one named Mountain.