Tl;dr: make sure you understand the difference between form (形), sound (音), and meaning (義). Some terms are also avoided in Chinese SE.
Syllable is a terminology of sound. In Chinese, the overwhelming majority of characters is monosyllabic, which is why the first two named columns are essentially identical. This is in stark contrast to Japanese for instance,...
According to ISO 639, Cantonese, Mandarin, Wu, etc. are languages, and Chinese is a macrolanguage.
It is easy and somehow correct to translate dialect <-> 方言, but it is not precisely accurate.
As far as Chinese is concerned, those called 方言 today once were languages and sounds like languages more than like dialects. But they share the same writing ...
Chinese do not consider American English a dialect
American English = 美式英語 (American style English) or 美國英語
British English = 正宗英語 (Authentic English), 英式英語 (British style English) or 英國英語
Both are English. We Canadian consider our English North American (北美洲) English - the same as 美國英語
American accent = 美國口音
British accent = 英國口音
The difference between ...
I believe all countries have dialects. Where a dialect stops and a language begins is unclear.
I would say the Central Government of a nation will concern itself with the national language, because it directly binds the people of a nation together.
Thus the notion: "A language is a dialect with an army and a navy."