Based on the photograph of the PCB, the input connections go to the top of the volume control and it's other end is ground. It would be safe to assume the input impedance is approximately the same as the value of the volume control. Look at it closely and it will have the value marked on it, probably as a letter and three digits, something like 103A which indicates 10K logarithmic track. The first two digits are the value, the third is the number of zeroes following it, for example 103 means 10,000 = 10K.
A summing amplifier can have zero gain or a higher gain, it is set by the scaling of the feedback resistor values. It will draw some current but it should be very small, probably less than 1mA so it shouldn't make much difference to battery life when compared to the 3,000mA the main IC can take.
The bluetooth adapter should work well with the summing amplifier although to be fair, it should work with a resistive isolator as well. The frequencies the advert quotes are sampling rates, and misleading too in the context of Bluetooth communicaton. They have litle relevance to the audio you hear through the amplifier.
Brian