I think when you parse this out you realize that there are a lot of other factors at play here, it’s not just a “belief in belief” thing.
Treating someone nicely has an influence on how they subsequently treat you and others. So it’s not so much that you’re believing someone is nice when they’re not, it’s that you’re believing that they do not have a fixed property state of “niceness”, that it is variable dependent on conditions, which you can then manipulate to promote niceness, for the benefit of yourself and others.
None of this is belief in belief. When you look closer you see that you are comparing two different things: how nice Bob has been in the past and how nice Bob will be in the present/future, dependent on what type of environment he is in, and you are thus modifying your behavior on the assumption that your contribution to the environment can make it such that Bob will be nice, or at least nicer. And there is evidence to support this assumption, so it’s not irrational to expect Bob to be(come) nice when treat him nicely accordingly.
It’s just misleading to phrase it as “I benefit from believing perople are nicer than they are,” because what you mean by the first “are” (will be) is not the same as what you mean by the second “are” (have been).
Sure, that’s true. I suppose you could have a split-brain person who is happy in one hemisphere and not in the other, or some such type of situation. I guess it just depends on what you’re looking for when you ask “is someone happy?” If you want a subjective feeling, then self-report data will be reliable. If you’re looking for specific physiological states or such, then self-report data may not be necessary, and may even contradict your findings. But it seems suspect to me that you would call it happiness if it did not correspond to a subjective feeling of happiness.