Hi,
1) Tom : There are many dialects in the Chinese language such as Cantonese and Hokkinese.
Why the is needed before Chinese language? (It is just the first time we mention it.) because there are many languages and we are specifying the Chinese one, not the German one, etc.
2)Tom: I have three pieces of advice.First........
Mary: Thank you for the advice.
"Advice" is uncountable noun. Why the is needed before this word? Just because something is uncountable, it doesn't necessarily mean you don't need an article.
3)Tom :Wow! Which city did you like the best?
Mary :I liked New York the best because there it has a lot of museums and shops to visit. I went to the headquaters of the United Nations, the statue of Liberty and the Metropolitan Museum.
Why the is needed before Metropolitan Museum? Isn't it a proper noun? There are lots of museums, here we mean specifically the Metropolitan one. Compare 'The Lincoln Memorial'. Or, from your own example, 'The United Nations'. Having said that, I admit that the use of articles with such proper names can sometimes be a little tricky and inconsistent.
Best wishes, Clive