What sort of thing is an object? Why does Wittgenstein never give us a clear account of what an object is?

At 4.0312, Wittgenstein says that his "fundamental idea" is that logical objects are not representative. What does this mean? How does it serve as a criticism of Frege and Russell?

What is Wittgenstein's philosophy of mathematics? How does it differ from the views of Frege and Russell?

What does Wittgenstein mean when he claims that a proposition of the form "A says that p" ought to be understood as "'p' says that p"? What can this position teach us about Wittgenstein's view of the self?

Explain Wittgenstein's distinction between the self of psychology and the metaphysical self. What bearing does this distinction have on the problem of solipsism?

Why does Wittgenstein claim we cannot put ethics into words? Is there any evidence for ascribing one or another ethical position to him?

Evaluate Wittgenstein's claim at the end of the Tractatus that the propositions contained therein are nonsense. What tensions in his work lead him to this conclusion? How can we make sense of this claim without diminishing the philosophical significance of his work?