(1) Inadequate. You shouldn't be writing from a place of incompetence. You have worked on your scholarly base and you are defending well-defined claims. Humility is all well and good, but without some faith in what you are affirming you won't be able to speak with authority.
(2) Tired. You will work better, write better, if you are well-rested. There is no point in fetishizing exhaustion. If after 2 hours you are tired, stop writing.
(3) Stupid. You might feel stupid because of something you are failing to understand. It's fine to feel frustrated by an intellectual challenge, but you have to know that you are smart enough to rise to it.
So no, none of these feelings is a sign that you are working productively. Inadequate, tired, and stupid is a good recipe for writer's block.