Must I repeat the prayers I performed previously in haste and without completing the recitation of the Fatiha, the Tashahhud, and the Tasbeeh, knowing that I used to pray them after an adhan from a muezzin who called the adhan before its time, and that my prayer has now improved?

You must treat the whispers you are experiencing with supplication and completely ignore them. Your prayer is valid and sufficient unless you have absolute certainty that it was performed before the time of prayer began, or that you intentionally omitted its pillars and obligations. For doubt after completing an act of worship is not to be heeded. However, if you become certain that an error occurred, then you must repeat those prayers. If you were unaware of this, you are not required to repeat them, given that you are suffering from whisperings (waswas (definition)).