Distance is not a problem since Britain can just ship supplies,troops and equipment from India.That is why for Britain to conquer China,it needs India,not to abandon it.India supplied much of the resources,troops,supplies and equipment to Britain’s other Imperial ventures including the two world wars.I have no idea why you insist on arguing that Britain needs to abandon India in order to rule China.IOTL,it was precisely because of the lost of India that Britain’s control of the rest of the empire became untenable.Only completely agree with 3) and 4) which is what I'm arguing for; China's distance makes it hard to conquer, requiring the British to surrender India as a result (at least most of it) and there would be indeed a lot of European infighting plus conflict with the US which surprisingly hasn't been mentioned that much.
1) depends on the highly overstated premise that the Chinese are more cohesive than the Indians when they weren't (look at the sectarian conflict between Daoists and Buddhists for instance, as well as the sizable minority populations not to mention geographical and political divisions among the Han Chinese as well), and 2)'s idea that the Chinese had higher availability of small arms is highly debatable seeing how the Mughals and Marathas used firearms as much as China and the former are even called a gunpowder empire by certain historians like Douglas Streusand.