Is gyro GY520 compatible with a servo JR DS8900g safely (used in mode 1 of the gyro but they are very hot after a flight with gy 520 and g7000t too!)

The rudder servo will be really hot with GY520 or G7000.  This is why 8900G servo using heat sink case.  This is probably normal.

About GY520's servo mode, Please choose the digital(1520).