Must I fast, and what is incumbent upon me to do after the death of my mother in a car accident in which I was driving and the other party was at fault?

If you caused the accident that led to your mother's death, then you are liable for blood money (diyya) and expiation (kaffara). However, if the error was on the part of the other party, then you are not liable for blood money or expiation; rather, the blood money and expiation are incumbent upon the one who committed the error.