Can we bridge Wi-Fi and WiMax network signals so that devices on them communicate?

Actually this is the main concept of WiMAX, work as a bridge between BroadBand and local wifi devices,   If you mean you want to connect between to different devices in different WiMAX devices, ISP company will not allowed it for security reasons, since they give the CPE public IP and no local IP is located.
and you can only connect through that public IP in otherword, it will be like you connect to anyother device in the world and you will not get benefit of the shared physical backhaule.