Reading a Open Loop Current sensor
What is the difference between Primary nominal RMS current and Primary
  current measuring range?


Both are per-part number metrics.  They both relate to full scale measurement range for a device.
"Primary nominal RMS current" is the recommended max RMS current.  It is also used in the equation for VOUT.
"Primary current measuring range" is the max DC current that can be resolved.


  If I can force some Vref, so how's the offset fixed? It will change as
  I force the Vref, right?


The datasheet indicates that you can force VREF to be between 1.5V and 2.8V; it is nominally 2.5V.  VOE is defined as VREF +/- 0.025V, so yes, as you change VREF you will change the output offset (VOE).