Tp-Link switch can turn on other device, the these other devices must be on once it get power . Actually, if you turn on TP-Link switch, the switch will let the powre pass through, so the device...

switch to a different location and then change it back, it should be able to sync, but if no, the last method should be reset to it's default settings and reconfigure it.

How did you setup the switch? What's the led status on the switch? You can try to watch the setup video for some help: https://www.tp-link.com/en/download/HS200_V1.html#video

it seems the device is broken, ask for replacement

372Mbps is the powerline link rate. What's the bandwidth given by your internet service provider? If you connect a PC to the switch by a cable ,what's the speed you can get? Normally, if you turn on...

If it can still be controlled by the APP, you may need to check the settings on your Echo APP, try to follow the FAQ for some help: https://www.tp-link.com/en/faq-944.html