I am neither American nor a lawyer, but I have looked at the US Constitution a bit so I'll take a stab at these. Of course, an actual scholar of the US constitution would have more correct answers:
1.
Article Five of the US Constitution specifies the manner in which the constitution can be amended. It expressly prohibits any amendment that would deprives a state of its equal suffrage in the Senate. Therefore, the Constitution itself prevents certain amendments to the Constitution. It stands to reason that, should you wish to change the Senate away from an equal number of Senators per state, you would need two amendments. One to allow such an amendment and then a second which would itself be that amendment.
That the Constitution provides a process for amendment is proof that its framers intended for it to be amended. That they specifically laid out certain things which could not be amended indicate that they intended for it to be possible to amend anything and everything else. That the amendment procedure was itself not included in the list of unamendable things includes it in the list of amendable things. Therefore the list of unamendable things is in the scope of amendments as something which may be amended.
Of course, later amendments may repeal earlier amendments.
2.
If a state ratified two conflicting amendments - A and B - I would say that the latter of the two ratifications would take precedence. Now, if Congress passed A first and then B, and B was ratified by enough states first and then A was ratified by enough states, I would say that you would have a nice little Constitutional crisis on your hands.
I think the rational solution would be to follow the Convention process for amendments as laid out in Article 5. That way the states can sort it out definitively, federal Congress be damned.
3.
No.
4.
Since I mention it earlier as a way to solve the conflicts between the 13th and Corwin amendments, the plain reading of the text suggests that each state legislature applies to hold a constitutional convention. The natural body to collect and manage these applications is Congress itself. When Congress has 2/3 of the States applying for such a convention they will determine the process for the convention.