Asami is full of surprises that why he is a man of mystery. Maybe that's how he know to show aki his love and affection or keep him from harm in that particular time . I don't think Asami find it offensive when aki call him name, actually he likes it,for example in one scene asami said to aki "you feel so good inside " and Aki said, what you saying idiot something like that and he look happy when that happened. Overall personally, things you mentioned are what make him interesting and captivating. It make you question his character and he always has a motive in a very thing he do as far as tabaka is concern. He is a typical bad boy and the type you love to hate but can't.
Error correct, things you mentioned are some of what make him interesting and captivating.
Proof of Asami's love (no particular order) and some are a little twisted.
1. Drugs Akihito to keep him safe.
2. Goes to Hong Kong to retrieve Akihito himself.
3. Shoots messenger (Naked Truth)
4. Forces Akihito to live with him. (With Asami an expression of love, with others it would be psycho).
5. Finds Akihito during his summer vacation.
6. Finds Akihito when he is chaperoning high school students.
7. Yukata & fireworks.
8. Lets Akihito to talk back and call him names.
9. Changes facial expressions once or twice.
10. Tells Kirishima to take Akihito and leave on the helicopter, to leave him behind.