Try using http://www.autohotkey.com/ with the following script:

^!b::
    MouseClick, left, , , 1, 0, D
    Sleep 5000
    MouseClick, left, , , 1, 0, U
return

This will click the left mouse button for 5 seconds when pressing ctrl-alt-b.

This is regardless of inputdevice. To find out which keycode your device sends use the built in "Key history and script info" and replace the "^!b::" with the keycode found, ex: "SC132::".

More information about MouseClick http://www.autohotkey.com/docs/commands/MouseClick.htm

Yes. To add a Bluetooth keyboard, go to Settings > Accessories > Manage Bluetooth Devices.

For a non-Bluetooth wireless keyboard to work, it would probably have to have its own wireless receiver that would plug into the console via USB.

It also supports USB keyboards. From page 31 of my PS3 owner's manual:

Using a USB keyboard

You can enter characters using a USB keyboard (sold separately). While the text entry screen is displayed, if any key on the connected USB keyboard is pressed, the text entry screen will enable you to use the USB keyboard.

Hint

You cannot use the predictive mode when using a USB keyboard.

Unfortunately, it looks like there aren't many games that natively support keyboard/mouse. I did find the Eagle Eye, a third-party adapter that allows you to use a USB keyboard/mouse in lieu of a controller regardless of whether or not the games supports it.