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!
First, Karna comes to the Ranghabhoomi.
"Vaisampayana continued, 'When the spectators, with eyes expanded with wonder, made way for that subjugator of hostile cities, Karna, that hero with his natural mail and face brightened with ear-rings, took up his bow and girded on his sword, and then entered the spacious lists, like a walking cliff. That far-famed destroyer of hostile hosts, the large-eyed Karna, was born of Pritha in her maidenhood. He was a portion of the hot-beamed Sun and his energy and prowess were like unto those of the lion, or the bull, or the leader of a herd of elephants. In splendour he resembled the Sun, in loveliness the Moon, and in energy the fire.
Kunti recognized that Arjuna and Karna were brothers and she swooned away but was later revived by Vidura.
And knowing the state of things, Kunti the daughter of Bhoja, swooned away. And by the help of female attendants, Vidura, versed in the lore of all duties, revived the insensible Kunti by sprinkling sandal-paste and water on her person. On being restored to consciousness, Kunti, seeing her two sons clad in mail, was seized with fear, but she could do nothing (to protect them).
Later, Karna was coronated as the king of Anga.
At that very moment, seated on a golden seat, with parched paddy and with flowers and water-pots and much gold, the mighty warrior Karna was installed king by Brahmanas versed in mantras. And the royal umbrella was held over his head, while Yak-tails waved around that redoubtable hero of graceful mien.
This made Kunti very happy.
And Kunti, recognising her son in Karna by the various auspicious marks on his person and beholding him installed in the sovereignty of Anga, was from motherly affection, very pleased.
So the thing is, Karna was recognized when he had his Kavacha Kundala, that too in Ranghabhoomi itself.
In Karna Parva, Duryodhana told Shalya that he thinks that Karna is not born in Suta order.
"'Duryodhana continued, "Having obtained all the celestial weapons and the boons that had been desired by him, Rama bowed unto Siva with his head. Obtaining the leave also of the gods that great ascetic went away. This is the old story that the rishi had recited. The descendant of Bhrigu gave the whole science of weapons unto the high-souled Karna, O tiger among kings with delighted heart. If Karna had any fault, O lord of Earth, the delighter of Bhrigu's race would never have given him his celestial weapons. I do not think that Karna could have been born in the Suta order.I think him to be the son of a god, born in the kshatriya order. I think that he was abandoned (in infancy) in order that the race in which he was born might be ascertained (by his features and feats). By no means, O Shalya, could this Karna have been born in the Suta order. With his (natural) earring and (natural) coat of mail, this mighty car-warrior of long arms, resembling Surya himself, could not be borne by a common woman even as a she-deer can never bear a tiger. His arms are massive, each resembling the trunk of a prince of elephants. Behold his chest that is so broad and capable of resisting every foe. Karna otherwise called Vaikartana, O king, cannot be an ordinary person. Endued with great valour, this disciple of Rama, O king of kings, is a high-souled personage.'"
He thought that Karna was son of a god and born in kshatriya order.