I intend to take a holiday to taipei on 21.10.2015 to 25.10.2015 how is the weather,

You can go to visit National Palace Museum, the 101 Building, Mt. Yangming... If time permits, you can travl further to visit Ali Mountain, Jade Mountain (Mt. Yushan), Sun Moon Lake...

For food, you can go to the Shilin Night Market, a very famous food street among visitors.

According to weather forecast, it will be mostly sunny with some light rains every now and then. Temp will be around 80F. Summer clothes are OK, or maybe a thin coat for night time. And of course rain gear.

No more typhoon? I would also like to go during the same period.

According to the latest weather forecast, no more typhoon will happen then. So it shall be safe enough to travel. Anyway, for your sake, do pay close attention to the weather reports before departure.