Help me understand the pinout of this 21" LED display driver
There is only one ground, and it is for all the connections. 
Possibly. It's not noted, in the datasheet, so you should assume it requires some form of input to work properly.
Unknown. It's not noted, so assume it requires an external 5V source.


I'm being vague because the answers to the questions you're asking are largely not in the documentation for the LED driver. It's possible the driver has internal pull-up/pull-downs that would make it operate without external controls inputs, when fed 12V, but it's not noted in the datasheet. 

You should contact the manufacturer, and ask for a proper datasheet.