What is the parameter of the power source that satisfies the inrush current of the load?
What is the unit of inrush current? 


Ampere. It's a current. Typically, you'd look at peak current.

As you can see from that, it's not really a meaningful thing to give on its own.


  How can we identify (thus test) the inrush current provision of a power supply?


Short circuit the output. Observe the current through the short with a fast measurement device.

Really, for most applications, source impedance is more useful a measure, I'd say.