My friend and i are planning to go to taipei in late september. Is it a good time to go over there? is it a rainy season over there?

Yes, I think so. The typhoon season would start to be in the ending period, so it will bother you a lot. The average temp can be around 26C. However, it may still rain a lot then. Take along raincoat in case. Besides, it can be a good doscount season. You can get many things with great discounts then.