Is what is happening—this alignment between my thoughts and the Quranic verses I hear from the recorder—such as hearing verses about reliance on God when hesitant, or verses about the answering of prayers when despairing, or verses about patience when afflicted, or reciting Surat Al-Kahf on Friday when thinking about it—considered a coincidence or a sign?

It is not strange for meanings to be repeated in the Quran; it guides the Muslim to what is most beneficial for him in his affairs. This is one of the blessings of frequent recitation and listening to it. Whenever a Muslim needs an admonisher or a reminder, he finds it in the Book of Allah. So, praise Allah for this divine guidance and mercy. It must be noted that deriving Islamic rulings from the Quran requires referring to people of knowledge.