You are right that most of the time we refer to people from the UK as 'British'. However, in fact, the correct term for a person from the UK is 'a UK citizen'. The UK is a political rather than a cultural entity. The UK is composed of Great Britain and Northern Ireland, so, strictly speaking, the term 'British' excludes citizens of Northern Ireland. People from England, Scotland and Wales are British, but people from Northern Ireland are not. All are UK citizens. And to answer your second question - no, you cannot say 'He is a Chinese' or 'He is a British'. These are adjectives. They are not nouns. You can say: 'He is British' or 'He is a British man/student/tourist'. In general, the only nationalities where the adjective and noun form are the same are those ending in 'n' or 'i'. For example, you can say 'He's a Korean' or 'He's a Pakistani'.

Have you finished your year-end exams? Successfully?

these are all adjectives, NOT nouns, so there is no article, 'a' or 'the' with them, only with the noun they qualify - a British girl, a Chinese city, a Japanese painting. UK refers to a collection of countries, and is seldom used as an adjective; the adjective is usually of the underlying country (Welsh, Irish ... English or British...); https://en.wikipedia.org/wiki/List_of_adjectival_and_demonymic_forms_for_countries_and_nations What do you call people from Hong Kong? I call them 'Honkers' haha

yes British is fine, as is 'a British person'. 'the Brits' or 'a Brit' is informal. There are definitions of 'UK', 'Great Britain', 'British Isles' which cover various combination of England, Southern Ireland, Northern Ireland, Wales, Scotland and the 'Island of Ireland' so sometimes you have to be sure what you're referring to. Some residents of some countries might not like being referred to incorrectly. The minefield of terminology is here! https://en.wikipedia.org/wiki/British_Isles_naming_dispute