How to apply a (Rush) Travel Visa in Taiwan (Nicaraguan passport)

Hi, , I'm Nicaraguan living in Taiwan, and i need to visit to Hong Kong in early January. I read the article from HK Government website and it says a visa usually takes 4-6 weeks, and I read your writing, the overseas one would take 4 working days, so i am confused.

1. Can I apply a Visa in Hong Kong Economic, Trade and Cultural Office on Taipei?
2. So I need a Rush visa or a normal visa if I need to arrive to HK in early January?
3. How much for a Rush Travel Visa?