How do I use a servo in an interrupt?
The problem is that the delay routine is blocking. It stops operation and blocks other things from happening. Have a look at the Blink without delay example in the example tab. (also linked below)
https://www.arduino.cc/en/Tutorial/BlinkWithoutDelay

What you need to do is to not block. Call the time checker often and check if the time you want delayed has run out. The perform the action needed to be done at that time. 

This is a more sophisticated way to deal with timed events. Also look at this
Demonstration code for several things at the same time.
https://forum.arduino.cc/index.php?topic=223286.0

Have fun learning. :)