{Nightviel Specter} : Can I cast ANY card that is exiled with this card? ie: Land, creatures, instants, etc.
It says you may PLAY anything exiled. Not specifically cast, so even lands are fair game(just remember, you can still only play one a turn). Basically, the card exiles their cards, giving you both the resources and the spells you want out of thier deck.
Do the cards go to the player's graveyard upon use? or do they stay exiled?
They go into their owner's graveyard upon resolution.
Yes.