The grounding pin is mainly for the chassis ground of record decks. However, Beograms with DIN cords don't need it, as the chassis ground is connected through the sleeve of the DIN plug. You would only need it to attach record players with RCA wiring.
The hum most probably is mechanical noise from the mains transformer - many Beomasters suffer from it when they get older. I'm afraid there's not much you can do about it, other than put it on a surface that doesn't resonate and amplify the hum. Often just relocating it a bit on the shelf or table helps.