If an independent clause stands on its own, is it still considered a clause?

An independent clause, by definition, can stand alone as a sentence.

By definition, a sentence must have at least ONE independent clause to be considered a sentence.

A SIMPLE sentence has ONE and ONLY ONE independent clause.

A COMPLEX sentence has ONE independent clause and at least one dependent clause.

A COMPOUND sentence has TWO or more independent clauses.

A COMPLEX-COMPOUND sentence has TWO or more independent clauses with at least ONE dependent clause.