Lol good point raised
Anyhow to answer
In those days when the kings won over states they often gave it to their children and they ruled over the actual main state of theirs.
Duryodhan was given the land of Anga by his father, he had the rights over it. He just gave it to Karna and made him the king. He did it with the consent of his father and Bheeshm.
But sometimes even I think, did he actually give the ownership onto Karna with full autonomy? Or was it something like a Kshatrap territory handed over (something like British gave Dominion status to many of its colonies, even India was so till 1950) if it was the former then I think he was actually a much bigger Danveer than is future bff, to let go an opportunity to become the king isn't easy.
About the second part he definitely ruled over Anga, we only know about him being with Duryodhan while the latter was planning plotting or fighting, it's but natural that he would invite his innermost circle and have them at his side during these times. Rest of the time, Karna remained in Anga Pradesh and Shakuni in Gandhaar