Hi @rottendoubt , Thanks.
I think that the link you cite will allow you to apply. I started here: General Visa Application .
I think that there are various circumstances that qualify a visitor for special entry visa. I think that all will require a letter of invitation from Taiwanese private enterprise or Taiwanese government agency. There may be other Forumosa>Legal>Visa & Residency threads such as Business visit (special entry permit) - #5 by rooftopclown that can tell you more.
For your other questions, see if you can find answers in the Gold Card threads or maybe Gold Card experts will answer.