I suspect you don't understand how signals add up. If you add a 1 kHz sinusoid to a 40 kHz block wave, the result is not a 40 to 41 kHz signal. In fact, a 40 kHz blockwave already has overtones at 80,120,160, ... kHz. But reconstructing the ~1Khz signal is trivial: just use a low-pass filter. You've got so much margin that you can any convenient cut-off frequency between 2 and 20 kHz. This eliminates not the base 40 khz signal but also overtones.
For resistor values, I believe the goal here is to attempt to match impedances or to minimize signal attenuation. Model the output and input impedances of your sources and load (just a nominal impedance as a resistor should be fine) and determine what the resulting voltages/currents will be to assess your level of loss; then either play with the values to minimize it or use the equations to solve directly.
Assuming your sources have the same nominal impedance, Zs, the resistors are the same value, ZR, and your load impedance is ZL (and if I'm doing my algebra correctly), your level of voltage attenuation (V/V, not dB) would be:
$$
A_v=\frac{(Z_S+Z_R+Z_L)}{(2\times Z_L+Z_S+Z_R)}
$$
The total output impedance of the sources and mixer as seen by the load will be:
$$
Z_{out}=\frac{Z_S+Z_R}{2}
$$
The input impedance seen by one source will be:
$$
Z_{in}=Z_R+(Z_L)||(Z_R+Z_S)
$$
If your next stage is a high input impedance amplifier, such as an opamp, emphasize keeping your voltage gain as high as possible. If this is directly driving a load, such as a speaker, try to match the impedances for maximum power transfer.
The pulldown resistor is almost definitely used to minimize popping when you plug/unplug something. These are very common in guitar pedals that use true bypass switching for that reason. If it is significantly higher value (e.g. an order of magnitude or more) than the other resistors used in the circuit, you should be able to ignore its effects on the above equations.
Worst case, buy a variety of resistors (they're cheap!) and play around with several values to see which work better than others.
Best Answer
I think you may be pushing the data sheet to extremes for a frequency of 100kHz. The nearest circuit in the data sheet that matches your requirements is this: -
This down converts to 450kHz and uses an op-amp on the output so immediately you don't need to worry about a bunch of inductors - just use the op-amp instead for servicing your needs. Should you require additional filtering - use more op-amp stages.
The above circuit down converts at 90MHz using a 90.45MHz local oscillator - the two remaining inductors are there to match impedances for the RF input. At 100kHz just use an op-amp to drive IN+ and don't worry about matching at all because at this frequency it just won't matter - the input op-amp I mentioned needs to be reasonably fast and feed it's output to the IN+ via something like a 220R resistor.