I'm having trouble understanding the bolded parts from a sentence from the first episode of Death Note:

本日正午過ぎ東京都渋谷(しぶや)区で⸺同居している25歳の女性に暴行を加え殺害したとして

Questions:

1. I'm assuming the single verb "同居している" makes up an adjectival relative clause, but what is it modifying? Is it "25", "歳", or "女性"?
2. I know 暴行を is a direct object, but is it modifying 加え or 殺害した or both?
3. For that matter, what is 加え殺害した? I know that 加え is the stem of 加える, and that 殺害 is being combined with する to form a verb. Is 加え a noun that's being combined with する also (alongside 殺害)? Or is the whole of 加え殺害した a single verb (if so, what does it mean)?