Karna's false characterization in the TV serials summarized (biggest myths about Karna)
1. Karna studied in gurukul of Dron with Kuru princes only. He was friend of Duryodhan from the childhood only and was jealous of Arjun from the Gurukul days only.
2. Karna didn't face any caste issues except he was denied by Dron his request to teach him Brahmaastra. Brahmaastra could be learned by Kshatriya only with certain pennance or Brahmacharya and otherwise only Brahmin could learn it because it was Brahmaastra. That's why he lied to Parashuram that he was Brahmin and served him with dedication to learn Brahmaastra.
3. He was Sutputra which means the son of Radha (Brahmin) and Adhirath (Kshatriya) - a mixture caste created by inter caste marriage of Brahmin-Kshatriya. He was not neglected or discriminated by the society for his lower Brahmin caste compared to pure Brahmins, but only Brahmaastra vidhya had such preconditions.
4. Karna was involved in the conspiracy or shadayantra of killing Bheem in the childhood by giving him poison.
5. Karna went to fight against Drupad to give gurudakshina to Dron but he along with Kauravas returned with failure.
6. Karna and Duryodhan knew each other before Rangbhoomi through Gurukul and Duryodhan was projecting Karna against Arjun and was trying to lift him up to develop him as his supporter from the childhood only.
7. Karna was actively and willingly involved in Lakshagrih conspiracy (he never repented it and also knew that Kunti will also get killed).
8. When Draupadi rejected Karna, she knew about the conspiracy of Lakshagrih.
9. Karna was also given a kingdom by the king Jarasandh and he had very good terms with Jarasandh.
10. Karna clearly uttered the words "wh**e" (Veshya) in Sanskrit (Bandhaki) for Draupadi and also prompted and ordered Dushasan to disrobe her and was continuously involved and laughed in evil way at every humiliation of Pandavas and Draupadi.
11. Karna was involved in the plan of sending Durvasa to Pandavas to give them curse.
12. Karna suggested the plan to Duryodhan to visit the forest for hunting and to make a show off of wealth and pleasure in front of poor Pandavas to further humiliate them.
13. Karna was surrounded and was defeated by Gandharvas and failed to save Duryodhan and he even ran away from the spot.
14. Karna many times abused Bhishma, Drona, Kripa and Vidur in front of them and on their back to Dhritarashtra raising question marks against their loyalty and impartiality and always encouraged Duryodhan for war.
15. Karna was not Danveer throughout his life out of his generosity but he vowed to follow Asur vrat during Pandavas' exile years (just a couple of years before war). As per this strict vrat, he couldn't say no to person coming to him with some demand which he could fulfil. He followed charity due to this vrat only which he took to be able to defeat Arjun (so it was with ambitions and ill intentions and was followed only for few years of life).
16. Karna gave his kavach kundal in charity to Indra to continue following his vrat but in return asked a dart or arrow which couldn't be countered in order to kill his invincible enemy. He agreed to give Kavach Kundal only under the condition of this exchange and not otherwise.
17. Karna was defeated by Arjun in Virat war and at that time, he did not have his kavach kundal but did have the shakti given by Indra which he could only use as last option when no other weapons work.
18. Karna gave promise to Kunti not to kill 4 Pandavas to follow his vrat but didn't give promise to spare Arjun because that was the very purpose for which he took the vow (and now he even knew that Arjun was his brother).
19. Krishna himself called Duryodhan a tree of adharma/evil and Karna to be the trunk of that tree (when he came on peace visit of Hastinapur).
20. Karna was involved in the plan of making Krishna on his peace visit a prisoner of Hastinapur.
21. Karna even boasted that he would win the war for Duryodhan by killing Arjun and even Krishna along with him.
22. Karna knew about his origin and birth story before Krishna told him. It was not Krishna who revealed his secret to him to make him emotionally weak.
23. Karna himself arrogantly opted out to fight under Bhishma and he even thought and uttered the words that he would be eager to enter the battle the moment Bhishma is slayed.
24. Karna was not weaponless when he was killed. Krishna didn't tell Arjun to break any rules. It was Karna who stopped Arjun until he could adjust the wheel and asked Arjun to obey the rules of war. Krishna directly addressed Karna and asked how he, who didn't observe any rules of morality during his lifeime, is expecting others to obey the rules of war. Karna continued fighting in rage after hearing these words and Arjun slayed him. So no rule was broken.
25. His love story with Vrushali is shown in detail in the TV serial which is not part of the epic but part of the novel written on him which completely made a hero of a villain just to create false sympathy.