I do not have Idea of how to control the servo to over the eggs every 10 minutes without affecting the reading data of the other two sensors (Humidity and Temperature).
Do you really need a servo to turn over the eggs every certain amount of time? Do you really need that angular control precision?
Maybe you can simplify things by using a regular motor with a simple cam attached to the shaft activating a microswitch to stop the motor after the angular rotation you want which is probably fixed and always the same. if the angular rotation required by your desing is less than 360 deg per egg turn, then you may need more than one microswitch.
You will just start the motor when required and then just monitor the input pins where the switches are connected with a simple if(digitalRead(SwitchPin)==LOW) on every loop. Your sensors will continue operating on every loop with no problem as the rate of change of the temp and humidity is way slower than the Arduino loop speed.