Valkia has in her text Quest. Action:

I understand that her Action can only be triggered when she is located in the Quest Zone but does the Quest also mean that she can only be played in the Quest Zone so Quest has two designations Play and Action location?

No, she can enter play in all zones, but as you said the action only works if she is located in the quest zone.

So is the only difference between an other card which has italicize Quest (meaning to be played out of hand only to Quest zone) is that Action follows it??????

Quest only = you can play this only in the QZ.

Quest = the following ability works only when the character is in the QZ.