MacOS – Strange behaviour from delete key on a non-apple keyboard

I have a fairly generic USB keyboard plugged into my MacBook Pro. The Delete key doesn't seem to do anything most of the time. When I try to create a shortcut using it (to display the key code) it acts as if it's dead. Other keys around it (Home/End/PgUp/PgDn) seem to work fine.

Now here's the really interesting part. When I push the key in text edit, it seems to do a delete-forward.

I want to use this key with Cmd (the Windows key on my keyboard) to move files to the Trash. Can anybody explain why this key is acting the way it is? Can anyone suggest a utility which will tell me which key I am pressing on my keyboard? I used to use xev on an X Windows system. Is there something like that on a Mac without X installed?

Actually, I want the Delete key, by itself to do what Cmd Bkspc does in Finder. It moves a file to the trash.

But the standard OS X keyboard shortcut window won't accept any of the keys in the 6-key block with (Ins/Del/Home/End/PgUp/PgDn)

It's interesting. When I first pull up the keyboard viewer, it shows a diagram of a standard Mac keyboard. As soon as I hit one of the above 6 keys, the map changes to an extended keyboard closer to what I have. But the diagram has my Cmd/Opt keys swapped.

Is there any way for me to tell the OS I am using an extended keyboard?

The frustrating thing is, Mac OS is training me to use that key. It does something useful in lots of built-in applications. But I can't assign it to a hot key.

iCal – deletes an appointment (Cmd+Backspace does the same)
textedit – deletes forward