Is it possible to watch Youtube videos on the Youtube App while multitasking
Use multi task option of your phone. Your screen will be split into 2 parts, you can watch Youtube and do other stuff. You can also change the formation of the screen so 90% of the screen is browser/email etc en 10% of screen will be youtube for listening music.

I am pretty sure Android Kitkat can do that – I am doing it right now.