Does this system require me to download an app on my phone, or connect to a local Wi-Fi router to function?

No. Tiny Traveler AI Classic does not require Wi-Fi, internet, or an app for live monitoring. The camera connects directly to the monitor.

Full Answer:
No. Tiny Traveler AI Classic does not need Wi-Fi, internet, or a phone app for basic use.
The camera connects directly to the monitor, so you can view the live video feed and use the main monitoring features right out of the box.
The companion app is only used for extra features, such as viewing saved files, uploading custom lullabies, and updating firmware. The app does not replace the monitor.