Your points proved one thing; Pandavas never recognized Karna which a common man with ordinary intelligence can do.
The question is whether Karna is Good or Bad, I am of the firm view he was not BAD.
Draupadi has longed for a husband who will have wisdom and moral values, will be strong and well built, a good archer, handsome and intelligent.
Karna is the only character in Mahabharata who has all these qualities. Also, all these qualities have been equally divided in Pandavas (Yudhistira for moral values, Bhima for physical strength, Arjuna for archery, Nakula is handsome and Sahadev is the most intelligent).
Karna is the best archer (next to Eklavya) and Arjuna is no match for him. Dronacharya knew that Karna is far superior than Arjuna, hence he denies to teach him archery lessons. Bhisma knew that Karna is superior to Arjuna and thus prevents him from entering the war during initial days.
On the 10th day of the battle, Arjuna slays Bheesma with the help of Shikhandi.
Then Karna goes to Bhisma and asks for forgiveness, that he insulted Draupadi and he should have prevented his "wicked" friend Duryodhana from insulting the
kulvadhu, who represents the
pride and glory of Kuruvansh. He tells Bheesma that he was taken aback, that he was burning inside because Draupadi prevented him from entering his Swyamvar and denied him the glory he deserves. He continues telling Bheesma that by calling Draupadi a "Whore", he has committed a grave "sin" and he begs for forgiveness.
To this Bheesma says
"Hey Karna, jyesth Kunti putra Karna, you have finally realized your mistake.
Ghayal nagin, ghayal sherni aur apamanit stree se daro.Yasaswi bhava..!"
Karna was taken by a shock. He didn't knew that Bheesma knows his real identity. He asks Bheesma that if he knew that he is the eldest Kunti Putra, why did he prevented him from entering the war? What is his fault?
Bheesma says
"Karna, my son, you and Arjuna are the greatest warriors Kuruvansh has seen after me. Duryodhana, Yudhistir, Bheema, Dushasana... they don't have the merit of being a guardian of Kuru throne.
There are two reasons why he doesn't kill Bheema, despite having all the options to do so.
- Karna has given his word to Kunti, that her 5 sons will remain alive. If he kills Bheema, he can't kill Arjuna.
- If Karna kills Bheema, he would do injustice to Draupadi's unstrangled hair. Draupadi has taken a vow that until and unless someone brings the blood of Dussasana's heart and wets her hair, she will never tie her hair. Bheema has made a vow that he will kill Dussasana and bring his hearts blood to Draupadi. If he kills Bheema in this battle, he will do injustice to Draupadi.
Was Draupadi in love with Karna? - Quora