I have a Logitech mouse that I can map the buttons with an app when in Light Speed mode, but my wireless Akko keyboard requires the cable to be plugged in to be able to remap the keys. Since the dongle is called “receiver”, I kinda assume it can only receive signals but cannot send them, but that doesn’t seem to be the case with the Logitech dongles.
It depends on the dongle. I know Logitech ones are definitely bidirectional since you can configure the dongle to support multiple devices and reconfigure them. In some (not all) keyboards it is indeed receive only, the keyboard has a RF transmitter and the other end is just, as you said, a receiver.