Q: can i use my apple id without a payment option?

No.

Yes, set payment type to none in settings/ iTunes AppStore.

In terms of the question, Klaus1 is correct.   You cannot use the card, but if none is available to you, you can use that.  I suppose it is being picky to say that but those are the facts.

how to set payment options to zero?

If you mean remove your credit card details, then on your computer's iTunes you should be able to edit your payment info by going into the Store > View Account menu option and logging into your account, and on your account's details page there should be a payment link. Or you can do it on an iOS device by tapping on your id in Settings > iTunes & App Store .

Changing payment info : http://support.apple.com/kb/HT1918

If you don't get the 'none' option on the payment details screen : http://support.apple.com/kb/TS5366