For good results on firmware updates, connect directly (!) to the adapter you want to update.

They've probably switched into Standby mode. This happens when nothing active is plugged into the LAN jacks.

The simple answer to your question is yes, use your own passphrase for the powerline encryption. You can do that via the PC utility with a typed-in password. Alternatively, you can use the button on...

This may well be true: Poorly designed devices, switching power supplies in particular, can introduce high frequency noise back into the mains circuitry, making powerline communications unreliable or...

2.0.0 is ancient. Do update them - use the tool software that came in the box, and download the latest firmware image from the TP-Link website.

It may work, but it will certainly violate local RF regulations. Such an item must absolutely be purchased locally.