I know how hard this time is for you and I see you're a realist, like me, and you know that you will be punched in the gut when your father passes, even though you know it will happen. I am so sorry you're going through this. But you're absolutely right to plan ahead, and I wish I had done more of that with my mother. She wouldn't discuss what she wanted, except cremation and a pastor to say something nice.
As far as the financial matters, if there is a will, then you should make sure you know where to find it. If there isn't a will, it's usually not too complicated as long as you don't have any evil family members (most of us have at least one!) who will try to muscle in on even a small amount of inheritance. If it's just you, your siblings and your mother, then I guess that your mother gets everything - maybe something for the children, but I'm not sure. My mother only had her 2 daughters, and we were adamant about splitting everything exactly in half, so it was fairly easy (though my mother's sister did steal money my mother had in my grandmother's name, the token evil family member -and it still burns me up to think about it - stealing from my 90 year old grandmother, who is still alive!) You have to get to a lawyer eventually and declare someone the administrator of the estate - your mother may want it to be you, so then you'd have to deal with disbursing the money. A lawyer can do everything for you and advise you on most stuff.
The one thing that I realize now is SO important is the actual funeral. I never liked funerals, never saw any sense in them, but when my mother died I wanted my mother's funeral to be a TRIBUTE to a wonderful person, it was a very significant ceremony to me suddenly, and you just don't have the time and/or energy to make it as beautiful as you would like. The night before the funeral, we were trying to pick out photos to display at a Powerpoint presentation and pick songs that my mother liked. I was so distraught that I just told my sister to pick out the photos because I just couldn't bear to look at them. And I thought of some music, but to this day I kick myself that I didn't think of "Morning Has Broken" or "Here Comes the Sun" - 2 songs that are so uplifting and that my mother loved so much. You just don't think of these things when the person is alive, and when you're blinded by grief, you can't think clearly.
Also, if you will have a clergyperson saying anything at the funeral, find out if there's someone your father would like or that he or you have a relationship with. My mother and I are not religious at all - she believed in God but not organized religion - so she wanted something nice and Godly but not too sectarian. I wanted the hospice clergy person, as my mother had talked to him and really felt inspired by him, but my sister got a recommendation for another guy and his eulogy was HORRIBLE! I felt like getting up and leaving in the middle of it - not for myself and my own beliefs, but because my mother would have HATED it. We even told him beforehand what my mother believed, and he just preached what HE believed, and he didn't even know my mother beforehand, so it was like an insult to her memory.
So please think about what you would like said about your father and how you will want to honor him at the funeral - and maybe start writing something now, if you want to say a few words, too. I know it's terrible to have to think of these things when he's still alive and it's very upsetting, but I wrote a quick eulogy for my mother 15 minutes before her cremation ceremony because I had no time to think before that and I didn't even realize that I would want to say something. But I desperately NEEDED to say something in her honor and the result was fine, but could have been better if I had thought of it before.
Sorry I did my usual rambling - hopefully a teensy bit of it may be helpful to you. We're all here for you in your time of need and I hope all your prayers about your father come true.
I wish you some peace and solace,