Dear Kirst
Of course you are normal, your feelings are all normal, you have lost a Dad that you loved so much. I lost mine 4 years ago and like you I loved him to bits. I still do. I still think about him, sometimes I talk to him (he hasn't answered me back yet), but it doesn't stop me. It was my birthday yesterday, I was 57, and I looked up to the sky and said "Thanks dad, for 57 happy years". Sometimes you will cry, the slightest little thing will set you off, or you might not cry for ages. I have never cried for my dad, but at times I do think about him very deeply. Just yesterday for example, my daugher drove up from Bristol to our home in Derbyshire, and we got into our usual discussion mode (she is just like my dad, always got something to say about the state of the world, and dad was just a working class man), I could hear his voice in hers, we argued (amicably) and discussed stuff for about 4 hours. I thought, "thank you dad for this wonderful grand-daughter of yours. She is a chip off the old block". I hope you can see your dad's personality in your own children. That might help a great deal.
Of course your dad will be forever in your heart. Love him as you can, for the wonderful dad that he was.
Love
Margaret