Is it safe to travel F&E inTaiwan in early Sept since this is still typhoon period?

It is safe.
Although Sep is still in the typhoon season, but the typhoon will not always happen. It is suggested to keep attention on the local weather forecast to see whether you will meet typhoon or not.
Usually, it is hard to meet one. BTW, if the typhoon is not serious, it will not affect your traveling. So take it easy.