Hi Elevick,
Those are good questions.
The volume control on a preamp or integrated amp is indeed not linear, and will approximate to some degree being logarithmic, which is necessary because our hearing mechanisms are to some approximation logarithmic.
Power amplifier gain, as you realize, is often expressed in terms of db, which is a logarithmic scale. However, what the amp is really doing is generating an output voltage that is directly proportional to the input voltage, meaning that the input voltage is simply multiplied by some numerical constant, and providing the capability of supplying the amount of current that the speaker's low impedance will draw at that output voltage.
In this case the W4S amps have a gain of 27db, which corresponds to a voltage gain of about 22.4 times, based on the 20(log(V1/V2)) relation between db and the ratio of two voltages. So what the amp is doing, within the limits of the maximum output voltage, current, and power that it can handle, is generating an output voltage that is 22.4 times greater than the input voltage, at any instant of time.
Viewed in that manner, I think you will see that if some other amplifier had a voltage gain of say 30 times, and we provide the input to it through a resistive divider which in conjunction with the amp's input impedance attenuates the signal by a factor of 22.4/30 = 0.75, then the two amps will be gain matched for any signal amplitude and preamp volume control setting that is within their capability.
Best regards,
-- Al