If that doesn't work, check your router specs, logs, and status. It's firewall may be blocking outgoing NTP requests from the tplink devices.

Not safely, you need all 3 wires. If they're not available the box needs to be re-wired.

It probably won't work there. You need a neutral wire, line in, and load going to the fixture. You might have power through fixture type wiring which is a problem for smart switches.

That's the response TP Link devices use when you try to set rules on a device that can't reach the internet/network time servers.

Sounds like a wiring problem, that the black wires aren't what you expected. You might try tracing them back to confirm one really is line in and the other goes direct to the fixture. It could also...

That's often a wiring problem, either an incorrect white (neutral) wire connection or trying to use the switch in a "power through fixture" circuit.