From what I understand the volitional form is often used to mean "let's do" something, e.g. 行こう can mean "let's go". Can this form be use when the speaker themself is not going to perform the action? For example, in English a teacher might say, "Let's all do well on the test tomorrow!", even though she isn't actually going to take the test herself (my Japanese is terrible, but something like 「明日は試験を退けよう！」)? Could you use the volitional form in this case?
A second, similar question, if you don't mind. Could the volitional form be used in a case where neither the speaker or the listener will perform the action? Such as in a science documentary, when the narrator might say something like "Let's try mixing sulphuric acid with sugar", even though the actual mixing is not being done by the narrator or the viewer.