Kolkatta, Mumbai and Dhaka are all official english names. also, it's Sankt-peterburg. Dacca, Bombay and Calcutta are all former names. and Bengaluru is Bangalore's official name
Yeah a lot of these need to be changed. All of the Chinese cities are what they're currently known as. The other quizzes here don't translate/spell them otherwise, either. Madras and Bombay are quite outdated names, as well. Pusan isn't an English translation, rather an alternative spelling. The ㅂ character in Hangul reads as both b/p.
Dhaka, Kolkata, Guangzhou, Mumbai, Bengaluru, Chengdu, Nanjing, Chennai, and Busan are also common in English. For a lot of these cities, their endonyms actually more common than the old exonyms you have listed here.