I don't know about the flights. Last I heard they had "charter flights" regularly flying back and forth, but they were only for Taiwanese and I heard that they were thinking about opening them to Chinese. I fly back and forth to Hong Kong and Macau relatively regularly from Taipei, although less frequently in the last year.
Everything I've read and heard about the ferries say that they are open only to Taiwanese, although I wouldn't be surprised if now they let Chinese use them. I know that they were talking about demilitarizing the islands and attracting Chinese tourists. But I don't know anyone in Fujian who has used them. My Taiwanese friends usually go home via Hong Kong and I've never seen any options to get to Taiwan from China that I can use, not that I'm interested in taking a ferry and a plane or a series of ferries anyway.
The one thing that you can be sure of in China is that the rules change and and with luck, persistance and guanxi you can even get over on the ones that don't.