Can Allah Almighty address a specific person during prayer, or is the feeling that Allah is swearing to stabilize a person's work and marriage and draw them closer just an illusion?

What you are experiencing is either an illusion and a delusion from the subconscious mind, or a whisper from Satan. Allah Almighty said: "And it is not for any human being that Allah should speak to him except by revelation or from behind a veil or by sending a messenger to reveal by His permission what He wills." We advise you not to pay attention to these thoughts and to persistently seek refuge with Allah.