I presume that Spark core needs to be connect to wifi in order to function. Is this true? If not, what are some ways I can use Spark core outside where theres no wifi signal?
No, the Spark Core, and Photon most likely, can function without a WiFi connection just as a normal microcontroller. On the http://docs.particle.io/core/firmware/#system-system-modes you want to look into System Modes (Advanced Topics). The mode you will, most likely want, is MANUAL mode