Language
Written
Dialects
Owing to the many mountains and rivers in China, travel was very difficult. As a result, many dialects arose. There are seven major dialect groups, but literally 100s of regionalects, or regional variations. There is a saying in Chinese, 十里不同言 shílǐbùtóngyán, or every ten miles a different language.
The dialects are, at least initially, mutually unintelligible, though a speaker of one can pick up another over time due to the overlap. Some linguists claim that if China were broken up into countries the way Europe is, these different dialects would be considered separate languages.
HK, Taiwan, Singapore
Despite the decision by the Chinese Communists to simplify Chinese characters, Hong Kong and Taiwan did not do so. Traditional characters are still used in those places. The Communist argument that the difficulty of Chinese characters was a reason for such a low literacy rate is clearly not true given that the literacy rate on both Hong Kong and Taiwan approaches 100%. Note also that calligraphy, an important Chinese art, is never written with simplified characters but always with traditional. At some point, Singapore adopted the simplified character set as well.
Pinyin
Pinyin is the romanization of Chinese. Up until the early part of the last century, various pinyin systems existed alongside each other, all created by foreign scholars. The Chinese decided to create one of their own, known as Hanyu Pinyin, and it is now the most widely used. Note that the reason you often see spellings of Chinese names and terms that do not adhere to the rules of Hanyu Pinyin is because they were adopted before it existed. An example is Lao Tzu for the Taoist philosopher 老子 laozi. It is common to see people from Taiwan with the surname 张 zhāng who write their name Chang in English. The earlier systems include Wade-Giles and Yale. In Taiwan they use a system that does not make use of the roman alphabet.
More to Explore
https://chinese.yabla.com/chinese-pinyin-chart.php
https://en.wikipedia.org/wiki/Pinyin