How can one deal with feelings of guilt and shortcomings towards a deceased relative, which lead to worry, sadness, delaying prayers, and thoughts of suicide, and how valid is the connection between a person's shortcomings and the death of a relative as a divine punishment?

You bear no responsibility for the death of your deceased. What you imagine are delusions cast by Satan into your heart, so you must ignore them and live your life normally. Nothing benefits your deceased except supplication, seeking forgiveness for them, and the acts of closeness (qurbat) you dedicate to them. You must adhere to God's law, remain obedient to Him, and abandon discontent and objection, for everything is by God's decree. Beware of neglecting prayer or delaying it from its time, and abandon the thought of suicide; there is nothing that justifies it, and you did not commit any negligence that warrants blame.