Ipad app icons shaking but won't delete, home button does not work, power off switch does not work

I just got a new ipad air and have started to add apps to it. I have added a couple of free apps which I have also deleted (moved to icloud). I have also a couple of apps (free & purchased) which I have on it now.

Now my problem:

I tried to remove another free app. I press and hold the icon. All app icons shake and display the 'x' for removing, but the 'x' for does not work on any of the icons. Also, after this, the home button does not work as the icons keep shaking even while I am pressing the button. And the power off switch on the side of the device does not work either. If I close the smart cover and reopen it shows the home display and all the icons still shaking (instead of showing the passcode sign-in display). Fortunately (well, fortune in the misfortune) if I press the home button and off switch a couple times each and close the smart cover and wait, the device awakes normally. Well, normally until I try to remove any app.

So what do I need to do to fix this?

Thanx

Brian