You can't blame your fallacies on me or anybody else, anchovies.
WRONG.
A republic is government by law (a constitution). That constitution specifies representatives (officers) in that government, what their powers are, the term of their service, the method by which they are elected, and also specifies how the owners of that constitution (the people for State constitutions and the States for the U.S. Constitution) may amend that constitution.
A government by constitution has NO powers outside of that specifically granted by it's constitution.
China is not a republic. It has no constitution. It is currently an oligarchy (dictatorship by committee).
Cuba is not a republic. It has no constitution. It is currently a dictatorship.
There is no such thing as a 'democratic republic'. A democracy is not a republic.
The United States is a federated republic. It is not and never was a democracy.
No. All officers and representatives in the United States are elected according to the procedures laid out in that Constitution. Their power and authority is only that granted by that same Constitution. Their term of service is specified by that same Constitution.
See Article I and the 14th amendment for the method of electing a Representative to Congress.
See Article I, the 14th amendment, and the 17th amendment for the method of electing a Senator.
See Article II and the 12th amendment for the method of electing a President.
Also see the 13th amendment, the 15th amendments, 19th amendment, the 20th amendment, the 22nd amendment, the 23rd amendment, the 24th amendment, and the 25th amendment.
A democracy has no constitution and no representatives. A democracy is government by popular vote, and is an unstable form of government.