I'm so sorry to hear about your dad. My father died 22 years ago, age 62. I hated to cry but every time I did I felt better, so cry your heart out. I've read that it's actually best to do so alone, that way you don't feel as if you should hold anything back or be strong for those around you. And we're always here for you. I found it almost impossible to sleep initially after my father's death. I'd have weird dreams, nightmares, then wake up and expect to see him, only to remember he was gone. So you may have strange feelings or experiences or whatever, just remember it's a normal part of the grieving process.
What may also help, in a few days when the arrangements are done and you're not quite as exhausted is to write in a journal, for 20 minutes, everything you're feeling. " Opening Up" by James W. Pennebaker is a good book which deals with emotional trauma and how the process of writing things down helps people cope. Pennebaker did several studies on the process, so it's pretty well documented.
Sorry I've written so much, I just wanted to express my sympathy. Hugs to you and your family
(((((((((((Termite))))))))))))))))))