Does TCP server has to run on public IP address only [on hold]

I have interfaced a GSM (Uni4 SIM800) module to a Raspberry-pi-3B module using AT commands to run a simple TCP server, and another pair of GSM and Rospberry-pi to run a TCP client. Now the Telecom operator(ISP) will assign an IP addresses to the GSM modules, then my questions are

  1. Are those assigned IP addresses are Public?.
  2. If yes and if the Server IP address is known, can my Client connect to that server?.
  3. If the assigned IP addresses are Private, can my Client connect to the Server? and How?.
  4. When IP address of server changes periodically, is there any way to find out the IP address of server from client before initiating the TCP connect sequence (like Host scan or using known MAC/IMEI address of the server).

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