Both curses and the references to the heart may seem a little old-fashioned, but perfectly native. "Curses in his heart" sounds like a good phrase for literature, poetry or religion. One would not say "in the back", but "in the back of his mind."

They're all surprisingly good for a machine translation except for the 'in the back' option. 'Curses in the heart' is okay, although, I feel we would more normally think of 'cursing in the mind.' But that becomes idiomatic and cultural to some degree-- in Chinese, are expressions like that typically discussed as involving the heart vs the mind? 'Outwardly agrees' and 'pretends to agree on the surface' are very natural expressions. If I had to rewrite it in another way, I would say: "He outwardly agrees, but, inside, he is fuming." Fuming means quietly but intensely angry/frustrated, similar to the word 'seething.'