After reading the posts by Minsc and SlaveOne, I'm gonna say that farseers are allowed to use mind war/eldritch storm multiple times in a turn. If you look at the Chaos codex (good call Minsc) you'll see that the powers there all say something like this: "This power can be used in the shooting phase instead of shooting," except for doombolt, which says that it may be used in the shooting phase instead of firing another ranged weapon and that it counts as a weapon. But before you go saying that we aren't talking about the chaos codex, just hear me out, because this provides valuable information on how to interpret the eldar codex.
Now we all know already that the BGB says that you are only allowed to fire one weapon per turn. However, it cannot be argued that using a psychic power is firing a weapon, because it simply isn't. So we know that the number of psychic powers one can use in the shooting phase is limited only by the rules of the codex and the particular psychic power in question, not the BGB's rules.
So the question is: what exactly does it mean to do something instead of firing a weapon? Using the chaos codex as an example, I think it is clear that to do something instead of firing a weapon does not mean that you somehow swap that action for the firing of a weapon on a one-to-one basis. The phrases "used in the shooting phase instead of shooting" and "used in the shooting phase instead of firing a weapon" are almost exactly the same, and have the same meaning, it's just that one seems a lot less restrictive than the other.
To put it simply, using these psychic powers in the shooting phase does not "replace" you firing a weapon. It is not firing a weapon at all, it is something entirely different. The only condition given in the powers' rules is that you do it instead of firing a weapon. So if you go to use that power what you would ask yourself is, "Am I firing a weapon or using this power?" If the answer is not that you are firing a weapon then you are fully eligible to use the power. Nowhere in there do you have to ask yourself, "Did I cast another psychic power in this shooting phase?" because the power's rules don't care if you did, it only cares if you fired a weapon, and using a psychic power is not firing a weapon, unless the psychic power specifically states that it is, like doombolt.
Using mind war and eldritch storm in one turn is perfectly 100% legal.