It's best to assume that all cabs take cash. That would be the safest as there are several cab companies in Singapore, some accept cards and some are cash only. Even if a cab company accepts cards, the cab driver may not want to (or give you the evil eye if you try to pay by card). There is also a 10% surcharge for paying by card.

Cabs from the airport to the city centre should be around S$30, and other than taking a cab to the Zoo, none of the rest of your cab rides should not cost more than that.

Very hard to tell you how much to change and we don't know what you want to do or how much you will buy. Just use the amounts mentioned here as a guide.