Must I fast after my friend died in a car accident and I survived, given that I had asked him to wear a seatbelt?

What you caused is unintentional killing, because your sudden movement to help your friend buckle his seatbelt caused severe panic, leading him to lose control of the car, causing it to overturn and him to die. You are required to fast for two consecutive months, and your Aqilah (male relatives on your father’s side) must pay the full Diyah (blood money) to the heirs of the deceased, as Allah Almighty says: (And it is not for a believer to kill a believer except by mistake. And whoever kills a believer by mistake – then the freeing of a believing slave and a compensation payment presented to his family, unless they give [it up as] charity. But if he was from a people hostile to you and he was a believer, then the freeing of a believing slave. And if he was from a people with whom you have a treaty, then a compensation payment presented to his family and the freeing of a believing slave. And whoever does not find [one or cannot afford it] – then a fast for two consecutive months as repentance to Allah. And Allah is ever Knowing and Wise) An-Nisa/92.