فِيمَ comes from فِي + مَا. When the interrogative مَا follows a preposition, its alif is often omitted. The question emphasizes the absence of a known motive.
قَتَلَ is an active past verb, “he killed”; قُتِلَ is passive past, “he was killed.” الْقَاتِلُ is an active participle and الْمَقْتُولُ a passive participle. This distinction clarifies the two roles.
وَالَّذِي نَفْسِي بِيَدِهِ is an oath, emphasizing the gravity of what follows.