I changed the keyboard on my Mac from the Apple Bluetooth keyboard to a wireless USB keyboard (Logitech K360). It seemed that this change did not help. However, after I turn off the Mac and restarting it (not just a soft reboot) and also turned the iPad off and then on again, everything seems to work as it should. The delete and direction keys work as they should.
It appears to me that there is an incompatibility between Parallels Access and the Apple keyboard.
I did install Parallels 9 and the older iPad application, called Parallels Mobile, no longer works. So, if you bought this and want to continue using it, you should probably not upgrade to version 9.