Yes, I agree; my comments are limited to the 3rd use of "would", as conveniently tabulated by Casiopea:
Auxiliary Verb: expresses past tense
 past of will
EX: "I will go," said Max. (reported speech: Max said he would go.)
Modal Auxiliary: expresses a mood
 to express a condition
EX: They would have been killed if they had gone.
 to express habitual action
EX: She would wait every evening for the bus.
 to express a polite request
EX: Would you like some more cake?
 to express probability
EX: She would be over fifty by now
 to express consent
EX: They would not help.
I might be inclined to move #3 out of "Modal Auxiliary", and into a new category.