Sorry to hear that your father is sick, Hunter Hawk.
A few additional thoughts, in no particular order.
Sometimes the funeral director will take care of getting the death certificate and getting it registered with the appropriate authority. They can order you copies.
If the deceased or their spouse is a veteran, they could qualify for burial in a veteran’s cemetery with a veteran’s plaque. Both are less expensive than regular plots and plaques. You’ll need to give his discharge papers to the funeral director. They’ll take copies.
Get photocopies of the death certificate as well. Some places will take a photocopy and they’re ten cents rather than twelve dollars each. Utilities, for instance, will take a photocopy, and if the bill’s in both names or if they’re getting a discount, the utilities will want to know.
If you feel it appropriate to ask about the possibility of organ donation, now is the time to do it.
If the hospital hasn’t already - get him to plan and sign an advance directive. A good directive answers a series of questions about what level of intervention should be done when he is no longer able to respond. It will also give someone medical power of attorney, authorizing them to make choices for him when he cannot. This will have to be notarized. Some hospitals have a notary on staff. Otherwise, you may need to have one come in.
The more that gets planned out ahead of time, the easier things will be. Funerals, for instance, are less expensive if they’re planned and paid in advance. My step-father, bless him, had a paid account with a local funeral home. There were still details to plan, but the basics had been covered.
Some retirement plans have a separate death benefit. You usually don’t have to request it separately, but check. Some retirement payments are reduced for surviving spouses. Some spouses do not qualify for continued benefits. This can be a rude surprise.
If your mother’s health insurance was through your father’s employment or retirement, it may discontinue or require payments. Not something that needs to be checked immediately, but something that should be checked.
Some mortgages have a small life insurance rider that pays off the balance of the mortgage in the case of the death of the main breadwinner. It would be an initialed line in the mortgage documents, if it’s there.
Our thoughts are with you.