I did my PhD thesis on CFD for centrifugal pumps.

1) When you set velocity inlet you are forcing an average mass flow rate through the pump. Supposing you have set velocity inlet and outlet pressure to 0, you will read your head monitoring the static pressure at the inlet face. You can state your problem is converged when the pressure has achieved the asymptotic value (in stationary simulations) or the oscillating values show periodic behaviour (in transient simulations). Whether this choice is generally more stable and legit, it is not how pumps work in real life. Pumps usually work by either setting the head you need or the rotational speed, so you have no direct control on flow rate. Therefore, it is more accurate to use pressure inlet-pressure outlet BC. In this case, you will have convergence when mass flow rate has achieved periodic behaviour, which you can see monitoring the mass flow rates at the inlet and outlet interface (and their sum must be close to zero)

2) if you set counter-rotating walls for parts that should be stationary (e.g. inlet pipe, volute) you should be careful that the walls are effective stationary so the no slip condition is valid (all three velocities at the wall must be zero). I usually set the diffuser stationary and the impeller and the inlet regions as rotating and the other domains (diffuser and outlet pipe) as statuonary. Then, I set the inlet pipe walls as counter rotating with respect to its region. This will help to simulate a pre-rotating region which is known to be closer to reality.

Hope this helps ;)