If a battery of a mobile device is completely empty (such as 0V and 0mA) and this mobile device is then put on a wireless power transmitter mat, how can the receiver send back packets at Ping phase?

The mobile device battery does not supply power to the P9020 receiver (Rx) IC.  The Rx IC is solely powered from the energy in the ping itself.  So, charging a mobile device from a completely dead battery state is no issue.