Kakashi is very much alive in the Boruto manga. The manga doesn't include his death. Maybe you got some misinformation or confused it with another character's fate. But for sure, Kakashi is around.
Kakashi's reaction would be complex. He is a man who has lost many people in his life. But Naruto was special. He would hold Naruto tightly, his hands trembling slightly. He might try to use some of his own chakra to keep Naruto alive a little longer, but deep down he knows it's futile. His face would show a mixture of pain, regret, and love. He would remember all the times he trained Naruto, all the lessons he taught him, and how Naruto had surpassed all expectations.
Kakashi might immediately offer a comforting presence. He could put his hand on Naruto's shoulder and just be there silently, letting Naruto know he's not alone.
Yes, he might. Kakashi is a complex character with diverse interests. Given his love for reading in general, it's not a stretch to think he could pick up a romance novel from time to time. He seems like the type who would be open to different genres to expand his knowledge and understanding of various emotions and relationships.
At first, Kakashi might try to distance himself from Team 7's possessiveness. He values his independence and doesn't want to feel smothered. However, as he realizes that their actions are coming from a place of deep love and loyalty, he starts to accept it more. He may even start to rely on them a little bit, for example, allowing them to help him with his paperwork or other small tasks that he usually does alone. This shows a new level of trust and closeness between them.