You seem to have double posted the same image in #1 and I suspect they should be different.
Does the transmitter and receiver need pairing together before use as I wonder what the button on the board image you posted does?
This is not half of the story though as you will somehow need to determine the protocol they are using and maybe the keys needed for a particular paring.
What you described is that one I am cosidering but not sure. Assume that already had the keys for paring. So how can I do to get/determine the protocol?
I presumed that the transmitter is dumb and always sends the same sequence. I've read somewhere that the used microcontroller (128K ram) doesn't have enough ram to use the full RX (64K) en TX (64K) buffers. It's always possible that it uses a small part of the FIFO however.