Yes you need a graphics card, the CPU doesnt have its own integrated graphics.
If gaming isnt a concern and this is just going to be a Home Theater machine, your probably better off getting something like an A8 APU.
Yes you will need a graphics card unless your motherboard has integrated graphics.
Have you bought anything yet?
If you tell me your country and budget i can recommend a graphics card.
If you haven't bought anything i can recommend an APU with built in graphics
Yes you need a dedicated graphics card. However, because you are not going to be gaming on it you can pick up a cheap $50 from NewEgg or Amazon and it would work just fine for movies and things not related to games.