Cosmological dynamics and thermodynamic behavior in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si17.svg" display="inline" id="d1e3093"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Q</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity: An analytical and observational approach