My friend and I will be going to Taipei during 2-6 September 2013

September is still in the typhoon season, but according to the previous records, typhoon is not frequent in that month. If you are very unlucky, you may meet one, but in general, it is hard to meet one during that time. It is suggested to pay more attention on the weather forecast before you travel.
If the typhoon is not very serious and level is below 3, the shops will not close, so please do not worry.