I currently have Lollipop 5.1.1. Is it possible to play a Youtube video in the background or while multitasking like checking email, use other apps or surf the web on Android? As of right now, I have to have keep the Youtube app open and can’t get the video to play in the background while I do other stuff on my phone.
No. I don’t think so; not using YouTube app. Try third party apps.
As already pointed out, you should try out third party solutions. I use this app for instance, Awesome Pop-up Video. It’s great and just gets the job done. If you’re rooted and on a device that doesn’t restrict apps a lot (Huaweis do) like my Note 3 then the app will directly pick up any YouTube videos you play and offer to play them directly from the notification shade. If you’re not rooted then simply clicking the YouTube share button and selecting Awesome Pop-up Video from the list of apps presented thereafter should do it. It always works.