How can one differentiate between the reality of disbelief and obsessive whispers (waswas), and what should be done when feeling afraid of disbelief due to actions or thoughts, or when repeatedly interrupting prayer as a result of these doubts?

Obsessive thoughts have taken hold of you, and their cure is to ignore them and not pay them any attention. Do not cut off your prayer, no matter how much Satan whispers to you that you spoke, or made a sound, or did something that invalidates your prayer. Continue your prayer and do not mind these whisperings. These thoughts do not harm you nor do they affect the soundness of your faith. Allah, in His mercy, has forgiven this Ummah for what its souls whisper, as long as it does not act upon it or speak of it. Repel these thoughts and ideas and do not dwell on them. You are on the right path as long as you strive against these whisperings.