Assuming both parallel pumps are identical, you calculate normally to find the absolute pressure at the pump suctions, using the actual flow in the common line and then dividing the flow as it physically does, calculating losses in each branch to find the suction pressure available at each pump...
Suck or push?
If you work in Absolute pressure, there is no suction.
If you work in Gauge pressure, relative to atmospheric, anything below atmospheric is "suction" or negative.
It makes no differnce on how the reduction on pressure is achieved, the pump sees NPSH, or absolute...
Need for check valves:
Check valves are necessary to prevent the backflow that would occur in most systems due to downstream pressure reversing the flow with a sudden loss of input pressure from the pump. Most systems do not suddenly depressurize, and would tend to backflow.
Leaving pump on...
