These two situations actually have two different outcomes. In the case where the Oblivion Ring that removed Garruk leaves the battlefield, he re-enters with his front face (Garruk Relentless) face up, with 3 loyalty counters. Rule 711.6 says
A double-faced card enters the battlefield with its front face up unless a spell or ability puts it onto the battlefield "transformed," in which case it enters the battlefield with its back face up.
When it re-enters from exile, it is a new object with no memory of its previous existence (see rule 400.7). Oblivion Ring doesn't say that it should enter transformed, so it enters with its front face up.
If you copy Garruk, Veil Cursed, the copy will enter as a Garruk, Veil Cursed, and because it has no default loyalty, it will in fact enter with 0 loyalty counters and die the next time state based actions are checked. Rule 711.3 says
Except for determining whether or not a permanent can transform, a spell, ability, or rule that needs information about a double-faced permanent sees only the information given by the face that's currently up.
Example: A Clone enters the battlefield as a copy of Wildblood Pack (the back face of a double-faced card). The Clone will be a copy of Wildblood Pack. Because the Clone is itself not a double-faced card, it can't transform.
The situation described in that example is exactly the same as the one you are asking about: if you copy a transforming card, you copy the information that is currently face up.