How to connect this 3 wire AC motor?
The hand-drawn diagram in your question shows blue and red reversed. It is possible that is an acceptable means of reversing the rotation of the motor. However it is also possible that the motor was manufactured with wire colors that do not match the manual. The resistance readings tend to indicate that interchanging the blue and red to reverse in not acceptable, but it might work even if it is not recommended by the manufacturer.

If the heat recovery unit is a manufactured item that you believe to have been installed and working properly previously, you should probably assume that the internal capacitor connection is correct. Connect the HI LO switch to white and black, respectively. Connect neutral to brown. Connect the switch and blue to power to run.

Testing:

If at all possible, measure the current when you first turn it on and compare with the rated current. Also check direction of rotation. That will prove if blue and red are properly selected assuming the product is viable at all. Resistance values indicate black/brown/5 must be hot or neutral and red, blue, 2, 3, 4 must be connected to the opposite side of the line.