China to Taiwan Flights

No there are no direct flights from China to Taiwan. There were some arranged as chartered flights during the Chinese New Year. That happened for the first time in January/February 2005...
So your choices are not many
Taipei --> Hong Kong ---> China cities
Taipei --> Jie Ju (Korea) --> Shanghai
Taipei --> Seoul --> Beijing or Shanghai
etc.

For info on China you could check my blog Living, Working and Travel China

Macau does not equal China when talking about international travel. I know, it doesn't make sense, but for purposes of immigration and flights, Hong Kong and Macau are not considered part of China.

Thus there's direct flights from Macau & Hong Kong to Taipei and flights from HK and Macau to anywhere in China are classified as international.

so your flight is direct.

Macau was not China, it was a Portugal territory before 20 Dec 1999. It retains much autonomy when it was returned to China. Macau has different immigration regulations, laws and currency from the rest of China.

Visit both Mainland China and Macau and you can tell a lot of differences.

Both HK and Macau are major transit points for travel between Mainland China and Taiwan.