Go from mainland China to Hong Kong and take a flight to Taiwan

The following is for reference

1. Is it possible to directly present the ticket and certificate without using the Hong Kong and Macau Permit?

As long as you present your Taiwan Entry Permit and air ticket, you do not need to use the Hong Kong and Macau Permit to go to Taiwan via Hong Kong.

2. If I stayed in Taiwan for nearly 7 days, and then returned to Hong Kong and entered the mainland for more than 7 days, does it count as staying in Hong Kong for more than 7 days?

A stay of 7 days in Hong Kong refers to the 7 days of entry into Hong Kong, and the days in Taiwan are not counted.