Has the neglecting daughter sinned against her father, whose news was cut off from her due to his involvement in suspicious activities, after which he died murdered because of them? And what should she do? And is there a sin upon the father for abandoning his children and shirking his responsibility towards them?

A father's shortcomings towards his children do not negate the obligation to honor him. Rather, honoring one's parents is obligatory even if they are disbelievers, as stated in the Quran. After the father's passing, he is honored by supplicating for him, seeking forgiveness for him, fulfilling his وصايا (testamentary bequests), maintaining ties with kin that are only connected through him, and showing respect to his friends, as mentioned in the Prophetic Hadith.