May i know,does NS accepts $0 order with no payment information on it?

@Krish pretty sure it does, although it might depend on your field settings. I know on the vendor bill side you can enter a zero dollar vendor bill and it will show as paid upon saving.

Yes, it does allow transactions with zero amount to be saved/created. It will have a closed/paid in full/etc. status and you won't be able to apply it to anything.