The true statement about the amendment process is:
Both the national government and the states are involved.
The amendment process as outlined in Article V of the U.S. Constitution requires both federal and state participation. An amendment can be proposed either by a two-thirds majority in both the House of Representatives and the Senate, or by a convention called for by two-thirds of the state legislatures. To be ratified, the amendment must then be approved by three-fourths of the state legislatures or by conventions in three-fourths of the states.
The other statements regarding unanimous consent or decisions made solely by a majority of Senators are incorrect. Unanimous consent from the states is not required, and the amendment process is not solely determined by the Senate or a new Constitutional convention.