Oguz, without knowing the lab conditions (latent, sensible loads), and the area of the US you are in, it is difficult to recommend a catchall solution. Liebert units are designed for precision temperature and humidity control. They are better suited for high sensible heat loads. I use them...
Q: Do we have to program the VFD to match only half the flow signal once we turn on second pump?
A: No. The flow should be measured at a point common to the discharge of all the pumps... 1 setpoint (adjustable), 1 feedback. The single (adjustable) setpoint and feedback should be common to all...