A single pump controlled by a VFD
This question is mostly about pump characteristics. The VFDs for single-phase motors that I am aware of do not provide full torque at reduced speeds, so they are suitable only for centrifugal pumps, not for positive displacement pumps. They are also suitable only for permanent split capacitor (PSC) and shaded-pole motors.

The power required to drive a centrifugal pump is given by:
Power = Flow X Pressure X Density / Efficiency X Unit of Measurement Constant.

Reducing the speed of a pump reduces the flow that it can deliver at any given pressure.

The efficiency of a motor powered by a VFD at rated speed and torque is only reduced only slightly below the motor's efficiency with utility power. Single-phase motor efficiencies vary quite a bit depending on power rating and design -- perhaps 60% to over 90%. Reducing the motor's speed and load reduces the efficiency. The efficiency drops gradually at first and then drops more rapidly to zero efficiency at zero speed.

Here are some PowerPoint slides that provide some basic information about VFDs and VFDs used in pump applications. http://vfdriveinfo.com/vfd-training-slides/