Taiwan

If you are familiar with China, you must know that there is hear of Mainland China and there is Taiwan.

It used to be a province of China and was once occupied by the Japanese in World War II.

all distinct groups of people need the definite article: the Chinese, the Americans, the French, the Aboriginal tribes of Australia...

In 1945, after the end of the Second World War, this the island was returned to China. at 1945.

The government of Taiwan has little influence on the journalism in Taiwan.

Because this is a special situation which may be complex for your reader, you should make your subject extra clear.

In other words, the televisions and newspapers can report almost anything everything as long as they want.

It looks like democratic.

However, the media is medias are full of bad news in order to attract people's attention, as people have less enthusiasm on good news.

He The professor was anxious about current situation of Taiwan's medias.

You haven't talked about this subject in a few sentences - repeat the object so that the reader knows who you are talking about. Also "media" is a nonplural noun.

He think the only way to get rid of this shortcoming is to improve the cultural quality of all Taiwanese the whole people.

Taiwan used to be a province of China and was once occupied by the Japanese in World War II.

Tonight, a professor came coming from Taiwan and gave us a lecture about the journalism of Taiwan.

The professor He was anxious about current situation of Taiwan's medias.

He thinks the only way to get rid of this shortcoming is to improve the cultural quality of all Taiwanese the whole people.

If you are familiar with China, you must have heard of mainland China and Taiwan.

I wouldn't capitalize "mainland" because it's not a name of a country, personally. You could say "the PRC". I probably would say something that avoids "you must" altogether, since it doesn't seem much like written language, but more like spoken language.

Taiwan is a big island in the south of China.

It used to be a province of China and was once occupied by the Japanese in World War II.

I would say, "It formerly was a province..." because it's a bit more formal, but I'm a bit more formal than most. :) It's a personal choice. "Used to be" is slang-ish in my opinion. I do not use it in writing.

After the end of the Second World War, in 1945, this island was returned to China at 1945.

This way works, too. The phrase "in 1945" needs to be a clause adding information to "after the end..." Otherwise, it seems like you're giving two times for the return.

Unexpectedly, a civil war broke out just after the war with Japan.

Tonight, a professor coming from Taiwan gave us a lecture about the journalism of Taiwan.

Unless you want to emphasize that the professor traveled for the lecture, I would just say he was "from Taiwan"

Their major goal is to obtain more profit.

I think using a more specific noun is appropriate.

However, the media is full of bad news in order to attract people's attention, as people have less interest in good news.

American English probably would use "because" instead of "as", but both are acceptable. I'd use either, but I'm more formal than average. I think "interest" is more important than "enthusiasm" here since "enthusiasm" usually describes something positive. You could say "enthusiasm about", though. "On" doesn't work with enthusiasm, in my opinion.

He was worried about current situation of Taiwan's medias.

I don't know how the professor thought, but "anxious" seems fairly strong and rather personal in this situation.

He think the only way to solve this problem is to improve the cultural quality of the whole people.

I'll have to think about whether I think "shortcoming" works here. Sigh, it's a bit late at night here!