They have a power cord, the bluetooth is just for connecting to audio devices

No, only connectable with a classic jack plug. I would recommend something more expensive for a PS5. They are OK for an office PC, but not recommendable for a great gaming experience.

Hello, BT stands for Bluetooth in many cases, including this one. This means that the BT version can be operated via Bluetooth. Kind regards

Goes both ways.

Yes, this speaker is equipped with a 3.5 mm audio jack (a 3.5 mm cable is included in the box), which allows it to be connected to various devices.