my family (7adults, 1child , 1 baby)will be going to taiwan on 24/7/13. I need help on the transport

We will reach taipei airport on 24/7/13 0600
What are the cheapest transport I can take to flying cow farm and whats the duration?
Next day will be leaving there to taichung city inn hotel the next day. How to get the?
Then from taichung to taipei.

I wish to take the bullet train. Which porition of my tour should I take? From airport to flying cow? Or flying cow to taichung? Or taichung to taipei? Or taipei to airport? How much and duration?

Anyplace which is a must to go there which is near to this place I will be at?

How to go ri yue tang, a theme park in taipei which I dunno the name, jiu fen, shi fen and I wish to go n fan tian deng.

What is the weather there now? I heard in august using will have typhoon.

Thanks inadvance for all the question ans.