Any permanent can have a +1/+1 counter put on it. Those counters won’t have any effect unless that permanent is or becomes a creature.

If you cast Earthen Arms for its awaken cost, a land you control can be both targets.

You can cast a spell with awaken for its mana cost and get only its first effect. If you cast a spell for its awaken cost, you’ll get both effects.

If the non-awaken part of the spell requires a target, you must choose a legal target. You can’t cast the spell if you can’t choose a legal target for each instance of the word “target” (though you only need a legal target for the awaken ability if you’re casting the spell for its awaken cost).

If a spell with awaken has multiple targets (including the land you control), and some but not all of those targets become illegal by the time the spell tries to resolve, the spell won’t affect the illegal targets in any way.

If the non-awaken part of the spell doesn’t require a target and you cast the spell for its awaken cost, then the spell won’t resolve if the target land you control becomes illegal before the spell resolves (such as due to being destroyed in response to the spell being cast).

The land will retain any other types, subtypes, or supertypes it previously had. It will also retain any mana abilities it had as a result of those subtypes. For example, a Forest that’s turned into a creature this way can still be tapped for {G}.

Awaken doesn’t give the land you control a color. As most lands are colorless, in most cases the resulting land creature will also be colorless.