What is the magic? I press the icon,it vibrates and I drag it slowly ti the red trash. Right? However it remains on the screen. One such delete had the icon appearing on the screen a 2nd time at the top. Solution?
Are you running a home-screen-replacement app, perhaps? Like Home++ or Panda? Maybe there's a bug in there which has prevented you from deleting icons from your home-screen?
That is truly weird, though... What about after a reboot? Have you tried rebooting, then immediately deleting those icons you want to delete?