写中文

Hi，大家好！(We seldom use "?" in greetings, and "Hi" is really common)
我想问一个问题：台湾人是中国人吗?为什么台湾人说中文?

Hi How are you guys?
I want to ask a question.Are taiwanese people chinese people?Why do taiwanese people speak chinese?

写中文

你好吗?
我要问一个问题台人是中国人吗?为什么台人说中文?

Hi How are you guys?
I want to ask a question.Are taiwanese people chinese people?Why do taiwanese people speak chinese?

改之后

↓

写中文

你好吗? 我要问一个问题，台湾人是中国人吗?为什么台湾人说中文?
Hi How are you guys? I want to ask a question.Are taiwanese people chinese people?Why do taiwanese people speak chinese?

写中文

你好吗?
我要问一个问题台人是中国人吗?为什么台人说中文?

Hi How are you guys?
I want to ask a question.__Are Taiwanese people considered Chinese people?  Why do Taiwanese people speak Chinese?

The problem is that you misunderstand the word "Chinese", like all western languages use the same word to mean "things from China" and the Chinese Race.  However, in the Chinese language itself, there are many subtle differences.  China is 中国, the Middle Kingdom (traditional translation), "Central Country" (if you want a more modern meaning, since China is no longer an empire).

In the old days, say before the communists took over, saying the Chinese (race) as 中国人 (people from China) is appropriate since there is only one China.  However due to politics and quirks of history, there are now two Chinas.  Each side claiming to be the legitimate government.

Of course, those in China says it is proper since they have the home court advantage.  However, you must not forget the Chinese (as a race) is a diaspora.  There are many Chinese born overseas.  So the term is not appropriate to them.  

As an example, you don't call yourself a Portuguese even you speak Portuguese!  You don't call yourself from Portugal but Brazilian.  Even if your family come from Portugal, most probably you call yourself Brazilian Portuguese.  Unless you are born in Portugal, otherwise others will look at you as being disloyal to your country.  So the same difference.

Use 华人, 漢族, 华夏, 漢人 if you are referring to the race.  As for the language, 中文 is fine.  So Taiwanese is ethnically Chinese if you want to be precise and avoid all political notions.

Therefore if you want to master a language, you must also learn its culture, history and traditions as well.