I have similar issues with shortcuts. Any suggested fixes useless. Affected only Windows 8.1. Any other OS works fine. After reboot all arrows on shortcuts missing.
Clean instal or upgrade makes no difference. So i guess Microsoft have no desire to fix this glitch.
Second bug about "move mouse to any corner",so on, i think this thingy named as out of box experience. So its just not running if users did some customizations right after fresh install of Windows 8.1. As result "you have new apps installed" not showing up on Start screen. However no problems if Windows 8.0 upgraded via Store.
About new apps not showing up on the Start screen; Microsoft did this by purpose since Windows 8.1, don't ask me why. They now show up in the All Apps view (click on the arrow pointing down in the lower left corner on the Start screen). If you want to have them on the Start screen, then you need to go there and rightclick on the app -> attach to Start menu.
As for the shortcut arrows glitch; I have a feeling Microsoft will ignore this just as the famous ugly black shadow icons that appear in dialogs and context menus: