Weather is an uncountable noun, and weather is a singular noun? Is the weather definite article a singular noun? Solve it, thank you!

Weather, weather, is really an uncountable noun.

In English grammar, whether a noun is singular or plural has nothing to do with whether it is preceded by the.

As a definite article, the is usually used in specific occasions. In addition, please remember that any noun in English (except proper nouns such as names and places) cannot be singular, that is, the, a (only countable nouns can be added after a), that, this or plural should be added before it.

In the example you gave, the weather refers to the weather in Taipei. This is a pronoun meaning "weather".

Grammar should be easy to learn, and exams are useful, although it will not be so boring to really communicate with foreigners in the future. . .