Measurement of RF Signal strength / phase difference
No it won't work. For a start it only has inputs that are sensitive down to -60dBm because it is intended for applying to circuits after the input from the antenna has been down-converted to an IF frequency and its power raised significantly.

The second problem I see is that you want it coupled to measure the input power on the BT antenna and this is going to kill-off the BT antenna signal quite badly - in effect you are busting-up the signal you are trying to measure because this device will look like another 50 ohm coupling on the antenna.

Thirdly, the BT receiver doesn't "transfer received RF signal to UART or USB" - it transfers demodulated data and this will not be indicative of the received signal strength.