I would have to see the words in context, but the description "apparent frequency" seems strange to me. The frequency your ear detects is exactly what the most sophisticated scientific instrument would measure. The Doppler shift is real in that the frequency your ear detects is really the sound frequency in your frame.
I would guess "apparent frequency" means that in your frame the frequency of the source is different to the frequency measured in the rest frame of the source. So you could argue that in your frame the frequency of the source "appears" to be different. However I would argue that it doesn't just "appear" to be different, it really is different!
You'll find the same sort of confusion when you start learning special relativity. In your inertial frame an object moving at nearly the speed of light has its length contracted, that is you will measure the moving object to be shorter than someone making the same measurement in the object's rest frame. But there's nothing "apparent" about it: in your frame the object really is shorter.
Here's a similar question which will be helpful to resolve your apparent perception of Doppler effect. Because, Doppler effect is real.
So would it be right to say that when the wave is reflected from B, we can think of it as a source kept on the car B?
No. Because the frequency has already been altered (probably increased) by the moving car and the wind (which can be found using classical velocity addition) and finally, the high frequency sound has been returned to B, which reflects it back - which again gets altered by velocity of B and wind flowing in opposite direction.
Due to the speed of the wind, can we substitute the relative velocity of the source and the receiver in the formula?
You should use the velocity addition formula. Don't forget to account for wind too...
Does the wavelength of sound change if the medium is moving? In particular, if the wind is blowing at the speed of sound in the same direction as sound, what would be it's wavelength?
The speed of sound is a constant at a particular medium. So, if the frequency of sound changes, the wavelength should also change in order for $c$ to be constant. If the wind is blowing the opposite direction to the source of sound at $c$ (no relativistics...), the wavelength is $0$. Because, always keep in mind the sound is pushing & pushing & pushing of the molecules. If there's an opposition pushing it with the same velocity, then its whole energy would be spent trying to oppose wind and finally FAIL...
Best Answer
The doppler shift causes a shift in wavelength at the origin of the wave (the frequency of the source never changes). This results in a shift in frequency for the observer.
In the link below you can see the emission of the wave for a moving source causes the wavelength to be shorter in front and longer behind. The actual source isn't changing in frequency. So it's a matter of relativity. To the traveling observer (in the source), only the wavelength is changing, to the stationary observer (experiencing the doppler shift) both frequency and wavelength have changed.
Lookang, Wikimedia commons. More simulations and applets here.