Use pump and compressor by splitting streams into liquid and gas
Correct

As the multi phase pumps are screw pumps
Correct

centrifugal pumps and centrifugal compressors can be used
Correct but consider that, as per my personal experience, the adiabatic efficiency for the compressor and pump must be <=25%.
The default value of Hysys is 75% and with this efficiency the power of the system (Pump+Compressor) is UNDERESTIMATE.
This my experience is with an supplier of multiphase pumps (Construction Phase of Project with Multiphase Pumps of 5000 SBPD (Liquid) + 60 mc/h (ACT Gas Flow).
The quantity 25% is an "rule of thumb" but i don't know if is equal for all the suppliers/cases