I'm travel to Taiwan between 08 Sept 15 to 20 Sept 15

It is too early to tell the exact weather data during that period. I read the weather records of the past years. It may rain a lot then with most moderate and light rain. Raincoat should be prepared. The temperature may range from 25C to 30C, still hot, so wear summer clothing.

Typhoon season extends until September. Typhoons can impede road travel, but usually it lasts just a day, maybe 2 at the most.