How can I tell if I can power NFC chip passively?
If by passively you mean that there is no need to have a battery (or other supply means) on the tag/card side, then yes, ISO/IEC 14443 always implies that.

ISO/IEC 14443 describes a way to communicate wirelessly between the reader and the tag/card, but also the way to provide power to the tag/card. The card reader has to comply fully with it, meaning that it must have the ability to power the cards, and the cards should be able to use this power.

Note that this doesn't prevent the tag to eventually embed its own battery, if the prower provided by the reader (which is very small) is not enough. This may be the case for some car ignition key fobs that include a battery.

The A700x family of chips are a special kind of microcontrollers usually embedded in smart cards (but they can also be embedded in regular packages to be used on a PCB, eventually). For the models that support ISEO/IEC14443 (A7005 and A7006), these chips can be powered wirelessly, yes. You don't have to hook them to a battery.