The correct option is "I and III only" because Statement I accurately reflects the constitutional provision that the Speaker continues in office until the first meeting of the new House after dissolution, ensuring continuity in parliamentary functions. Statement III is also correct as it stipulates the process for the removal of the Speaker and the necessary notice period, aligning with the procedural requirements set forth in the Constitution. However, Statement II is incorrect because the Constitution does not mandate that a Speaker resign from their political party upon election; rather, they are expected to be impartial and may choose to resign voluntarily. This understanding aligns with the UPSC's focus on constitutional provisions and the functioning of parliamentary democracy in India.