Why can microphone be much smaller than wavelength of sound? For sound from 20Hz to 20kHz, wavelength is 17m to 17mm, for sound at 2kHz, wavelength is 17cm.
And I saw tiny microphone which is much smaller than that. In electromagnetic, there is a smallest size for antenna of each wavelength (half wavelength???). And there is a law (IIRC) that if sampling frequency is smaller than half of the signal, than it is not possible to reconstruct the signal.
How can microphone size is much smaller than the wavelength? E.g. the head of the mic of singer, I think it is smaller than 1 cm
 A: A microphone is a transducer that converts variations in air pressure from sound waves into electrical signals.
Air pressure varies as the wavefront passes into the diaphragm (or the ribbon, or the condenser) of the microphone.  The diaphragm needn't be as long as the wavelength, as it senses the wave from a "head-on" perspective rather than "looking at it" from the side.   
A: Microphones transform the pressure wave of sound to an electric signal.
The wavelength of the sound wave tells us the distance over which the wave's shape repeats itself in space. The frequency measures the changes in the medium in time. 
As the sound wave passes, the molecules of the microphone vibrate in place ,according to the frequency, like a harmonic oscillator,  and this vibration can be utilized to generate an electromagnetic signal. The spatial dimensions are not limited by the sound's wavelength but by the elasticity and the molecular bonding  that responds to the frequency of the  incoming wave.
A: Some thoughts on the subject:
The key difference between a microphone and an antenna is that the microphone is sealed from the back - it senses a pressure difference between the front and the back of the membrane regardless of the extent of that pressure region.
If you have a small membrane that is not sealed from behind, then at low frequencies it will "bathe" in the slowly varying pressure and will indeed show little signal; a larger membrane would prevent the pressure from "leaking around the back" and thus be more efficient at capturing the energy from the incident sound wave. It is true that a larger membrane can "harvest" more energy - but typically the transducers are so effective that they don't need to be large in order to get a good low-noise signal pickup.
A conventional antenna is immersed in the electromagnetic field - current induced depends on the potential difference from one end to the other (integral of electric field). This value increases with increasing length of the antenna until you reach a quarter wavelength (for a monopole) or half wavelength (for a dipole). 
In this context it is worth noting that the lateral displacement of the membrane is very, very small - in other words, the membrane won't move enough to compress the air behind it.
