They both landed successfully and Ingenuity was deployed. Perseverance drove away, and then failed. Could Ingenuity survive on its own?
No. Perseverance is the communications relay for Ingenuity.
Ingenuity uses essentially ZigBee to communicate, the same protocol that possibly your smart bulbs use. ZigBee has a range of about 300m line-of-sight without obstructions which is just a tiny bit too short for communicating with Earth.