What is the significance of a prolonged illness and death on a Friday, and how can children honor their deceased father, and what are they advised to do at the burial?

May Allah reward your condolences and forgive your father. As for the questions you asked, they have been answered in previous fatwas, as follows:

1. Allah decrees nothing for a believer except that it is good for him. 2. Dying on Friday is a sign of a good ending. 3. Filial piety does not cease, even after the death of one's parents. 4. What should be done for parents after their death. 5. What is legislated to be done at and after death, and what is not.