Well, normally such a thing like a keyboard special keys is handled by a keyboard driver. I have a Bluetooth 6000 keyboard and it seems to work OK. Looks like two drivers loaded, kbclass.sys and kbdhid.sys. I do not believe this keyboard uses the iType software, but it is loaded (I do have another, non-wireless keyboard).
The fact your remote doesn't work would seem to be related to the keyboard situation.
You have, of course, checked your batteries. Can you adjust the volume of your speakers using the speaker volume or the speaker icon in the system tray?
Do you see a volume bar on the screen when you hit a volume key on the keyboard? Can you mute the speakers?
Does your system use a mixer other than Windows? For instance, mine has a Realtek mixer.