No ferry from Fuzhou, you should departe from Xiamen. Xiamen's 厦金客运码头 (now 厦门海峡邮轮中心) have direct ferry to Tai Chung and Keelung City.However, the ferry boats are almost available on Tursday, only one in Saturday.

From Fuzhou:
Travel to Matsu Island (Taiwanese county) first, 1.5 hr away by boat. From Matsu to Keelung takes 11 hrs, no boat on Tuesday

From Xiamen:
According to phone enquiry to Xiamen International Ferry Centre (厦门国际邮轮中心) just now :-
Xiamen to Keelung - leaves Thursday 1800, arr. morning, return trip departs on Monday
Xiamen to Taichung - leaves Monday 1800 or Tuesday 1200

Info to these trips is not on their website.
Phone enquiry: ( 86) 592 202251 6 or 7 (chinese only?)

Took me weeks to gather all this.

Good afternoon, fellas!
I'm planning to go to China as you described!
first to Matsu then to Fuzhou. But I don't have any clue how I can buy tickets from Matsu to Fuzhou. no info on website.
please, share if you know something...

Looks like nationals from countries other than from Fujian are now allowed to visit Kinmen, Taiwan. Am I correct? Someone from this thread says that only Fujian nationals are allowed whereas there's a news report that other nationals are now allowed (obsolete situation?). Which is correct? Planning to go to Xiamen using ferry service from Kinmen island after domestic flight from Taipei. This is feasible. right?