I was in the same position a year ago and I indeed rang the school office for clarifications!
Anyway, going by last year's rules - yes, the cardigan should be the one with the school logo. On the other hand, the only polo that needs to be with a logo is the PE one; for the "standard" uniform most children just use plain white, un-logoed ones (also because the logo-ed ones are not 100% cotton - at least this was a big driver for me).
I am not entirely sure about PE bags/book bags as I wouldn't have known where to find another one, so it didn't dawn on me to check if alternatives were allowed
Anyway, do call them: the office staff are very friendly and helpful! Also, they recently introduced a new uniform policy; from a quick read it seemed to be just enforcing the principles, but better check just in case I missed something...