For Roman Numeral questions (the problem solving questions that require you to assess the veracity of three statements) do I have to handle the statements in the order given?
No. Test the statements in whatever order you find the easiest. Once you have determined the veracity of a statement, eliminate answer choices accordingly. For example, if you have determined that Statement I must be true, and the question asks which of the choices must be true, eliminate choices that do not contain Statement I. Sometimes you can pick numbers to determine the validity of each of the statements.