Do Senate rules violate the U.S. Constitutional provision which says the Senate may determine its own rules?

Continuing the discussion from Please explain your Senate rules to me:

~Max

The Senate is a creature of the Constitution; the Senate’s “nearly absolute power” is limited by the Constitution.

A hypothetical Senate rule prohibiting the appointment of a President pro tempore would necessarily be unconstitutional, because it violates the Constitution’s directive: “The Senate shall chuse […] a President pro tempore, in the Absence of the Vice President, or when he shall exercise the Office of President of the United States.” (Likewise, Congress’s power to direct the manner of appointing D.C.'s electors cannot be construed so as to prevent D.C. from appointing electors, which is required by the Constitution.)

A hypothetical Senate rule may not, without violating the Constitution, deny the right, provided for by the Constitution, for a minority of Members to compel the Attendance of absent Members. (This is despite the explicit allowance of each House to provide the Manner and Penalties for a minority to compel attendance of absent Members. Congress’s power to make Laws necessary and proper for carrying into execution Powers vested in a Department or Officer of the United States cannot be construed so as to deny, in practice or in full, the President’s constitutional right to require the written opinion of the his department heads).

A hypothetical Senate rule may not, without violating the Constitution, deny the President his constitutional right to, on extraordinary Occasions, convene both Houses, or either of them.

&etc.

~Max