Pneumatic microvalves are widely used key components for automating liquid manipulation and flow control in microfluidics for more than one decade. Due to their robust operations and the ease of fabrication, tremendous microfluidic systems have been developed with the multiple microvalves for higher throughput and extended functionalities. Therefore, operation performance of the microvalves in the integrated microfluidic devices is crucial to the related applications, in fields such as micro-flows, cell analyses, drug discovery, and physical/chemical detections. It has been reported that operation performance of the microvalves are highly sensitive to the device configuration and pressurization scheme. This implies the further development of integrated microfluidics with a larger number of the valves may suffer the problems of undetermined microvalve behaviors during operations, which can become an unavoidable hurdle in the device design and optimization processes. Herein, we characterize responses of the individual microvalves for different operation configurations, e.g., membrane thicknesses and driving pressures. We investigate also the effects in microfluidics integrated with the more valves, through experiments, modeling and simulations. We show that dynamics of the microvalves is indeed influenced by the configurations, levels of design complexity and positions in the devices. Overall, taken dynamics of the microvalve responses into considerations, this work provides insights and guidelines for better designs of integrated microfluidics for the future applications requiring higher throughput and improved operation performance.