So to hear of your loss, chocolatestar and especially the suddenness of it.
I still talk to my Nanna and my Mum, in my head, in my dreams sometimes too and whenever I visit their grave. Sometimes I "feel" an answer from them, if that doesn't sound too kooky - it's probably just my unconscious mind telling me the answer but I like to think it's them answering me.
You can cope because you will have to - whatever your belief system will support in terms of where your Dad has gone will help you in the long run. I believe in a spirit dimension and believe that I will see my grandparents and my Mum there again some day, and that they are reunited there.
I also can still "hear" their voices (Grandad's too), sometimes just as oft-repeated phrases, but it's their voices all right and that comforts me.
At this stage, you are going to have all sorts of emotions to deal with - let them happen, give yourself time, but don't let them overwhelm you. I hope you have someone in RL to talk to and comfort you. If not, maybe Cruse could be of some use to you.
Big (((hugs))) to you - it's a horrible place you're in at the moment but eventually life will start to return to something like normal, albeit a different normal.