Salvete iteum, Tergeste et alii
Concerning your question about the Taiwanese writing system, I might have some thoughts to share with you, Tergeste.
It is a complex history. In that way that, for starters, there have been and still are numerous indigenous dialects (wheather we should speak of languages is an ongoing debate), each with its own organisation. When it comes to the writing system, Taiwan is now mainly a Hancha- nation, like mainland China, meaning they use Chinese characters. But here, it becomes complex. It is certain that they use characters of Classical Chinese without simplifying them like the PRC has done. So this is an answer to your question.
The question in my view is how long will this situation continue? There is a tendency on Taiwan of strong relations with Mandarin Chinese now, through education etc. They are getting closer, and at a certain point in the future, a merger is not unthinkable. But it remains to be seen, because there will be nationalism involved... Where that would end with regards to the writing system, I can only guess. The logical thing would be to adopt the simplified characters. But maybe that is wishfull thinking on my part.
What is certain, is the fact that the best language education in and on Mandarin Chinese is on Taiwan, where it exists next to the many dialects spoken in Taiwan. But we can divide them into four major categories which are popular to most of Taiwanese. Apart from Mandarin, they are: Fukienese, Hakanese, and Cantonese.
I hope this was a usefull contribution. I don't know if my answer is as it should be, but it is a complex matter and I am only a student of limited knowledge.
Optime vale.
Menc