Karna was born with divine Kavach and Kundala which is said to be brilliant and unique among all the astra shastras. So, how come throughout all stages of his life, nobody inquired/acknowledged that he cannot be a normal person, and at very least should be a Kshatriya warrior?
It's not true that "throughout all stages of his life, nobody inquired/acknowledged that he cannot be a normal person".
Duryodhana acknowledged this when Karna first time entered in the arena to challenge Arjuna during childhood. This is explained in Mahabharata: Adi Parva: Sambhava Parva: Chapter 139.
Krishna, Kunti, Bhishma, Narada and Krishna-Dwaipayana were aware of the fact that Karna was Kunti's son:
[Vasudeva said,] Thou, O Karna, hast been born in this way. Thou art, therefore, morally the son of Pandu.
Kunti said, 'Thou art Kunti's son, and not Radha's. Nor is Adhiratha thy father. Thou, O Karna, art not born in the Suta order. Believe what I say. Thou wert brought forth by me while a maiden. I held thee first in my womb. O son, thou wert born in the palace of Kuntiraja. O Karna, that divine Surya who blazeth forth in light and maketh everything visible, O foremost of all wielders of weapons, begat thee upon me.
[Bhishma said] Thou art Kunti's son, not Radha's! Nor is Adhiratha thy father! O thou of mighty arms, I heard all this about thee from Narada as also from Krishna-Dwaipayana! Without doubt, all this is true! I tell thee truly, O son, that I bear thee no malice! It was only for abating thy energy that I used to say such harsh words to thee!