Competent lawyers who draft estate planning documents such as a Will generally also drafting of Powers of Attorney, Health Care Proxyas and Living Wills to avoid the very difficult situation that your sick father has left for you.
You neglected to mention what state you are in and there may be remedies provided in your local jurisdiction, but I will address the general case. I happen to be licensed in Pennsylvania.
To take care of his expenses out of his funds, without a Power of Attorney, you most likely will have to go into court (probably Orphans' Court which is a special court that handles such family financial matters in most jurisdictions) to be appointed as guardian. This is done after a hearing in which you prove your father's incomeptence. Not a cheap or fast endeavor.
One suggestion I might make is that, and I am trying to say this sensitively, if your father is likely to pass away in the near future, you might simply to pay his expenses out of your own funds, and keep a record of all of your expenses and keep receipts -- ultimately his estate will be able to reimburse you for these bills paid on his behalf.
As for dealing with the hospital without a living will or health care proxy, hospitals have varying policies. Hopefully yours will be considerate and compassionate and keep you involved in decisions rather than merely informed.
I wish you well in this very difficult time.