First, the problem of free will is like a good infinite puzzle — for every good argument one can find, someone else may come up with a wonderful counter argument — and therefore what I write below is naturally arguable.
The problem of free will is tightly linked with that of moral responsibility, in the context of living in a society. and this link can be used to evaluate cases such as the ones you bring up.
Another point is that it is not so much about what you think and desire or believe that you think and desire (who can tell the difference?) but about what you eventually do in the real world — and that can include thoughts that were expressed by speech.
To see this, imagine that you need to press a button to save the life of someone you deeply hate. it does not really matter what went inside your head, the back and forth considerations, the resolution that you made and the last minute change of mind — what matters is what you eventually did.
back to the problem of moral responsibility — I like to think about it in analogy to spinning tops. that is, to think of a person as a kind of spinning top. you are considered morally responsible for what you do if you are a spinning top that is expected to handle the bumps you are likely to encounter in the society you live in without toppling down.
the spinning top is also a nice analogy since it involves a "mysterious" buffering between the physical environment and its own state or behavior — it really isn't trivial to understand why gyroscopes work the way they do — for example, most videos on the subject in youtube, including by some professors contain errors.
anyway, if I apply this to your examples, then it seems that in all cases except case #5, the person involved does not have compatibilist free will.
it depends of course on the problem at hand. if it is just about moving one's hand, then someone might say to the shackled person "hey, you do have free will! you can rattle your shackles if you want to, or at least show some interest by trying to fight your shackles".
but we can suppose that in all cases the person involved had to press some button and ask ourselves why they did not press it, and if they are morally responsible for not pressing it.
As for case #5, we can ask our selves how a court would handle such a case.
A court might look into the case and declare, "it was a mistake to assume this person is morally responsible for what he does — we need to lock him up because he is clearly not capable of being a morally responsible agent."
or "despite his history, it was still reasonable to expect this person to behave in such ansand such ways — we need to punish him because we believe it is reasonable to consider him morally responsible for what he did, despite his history."
or "we will give him a reduced punishment because we realize how his particular history affected his choices."
or "take this kid home, his parents should be held responsible for what happened."
Finally, I do not agree with the link you assume between physicalism and compatibilism. for example I am not a physicalist, and yet I find compatibilism an interesting view.
It is not true that dualists necessarily believe their psychology is non material or non physical. see Chalmers for example — for him one's cognitive processes are all part of the easy problem of consciousness.