how to correctly determine false alarm rate (in a specific experimental setup)
Check out chapter 3 of Macmillan and Creelman on rating scales. You have 3 ratings: left arrow (very confident it is on the left), space bar (not sure), right arrow (very confident it is on the right). You also have non-responses which may be equivalent to a space bar "not sure" or might be something else. I would probably want to know more about why they did not respond (and how often) before deciding what to do.

You also have 3 stimulus types (LVF-word, RVF-word, and double non-word) which makes things harder and I don't think is covered in M &amp; C. That said, you can extend their examples to 3 stimuli pretty easily. The index of sensitivity d' is a measure of distance between two distributions. It sounds like you want to know the distance between the LVF-word and double non-word distributions relative to the distance between the RVF-word and double non-word distributions, but maybe you only care about the LVF-word and RVF-word comparison.