How does the control-board on small drones govern their flight?
Maneuverability with this kind of drone comes with their small size and high thrust-to-weight ratio. When you scale such a dynamic system, the time scales with the square root of size, so the smaller the drone, the higher its agility.

Can it do automatic stall recovery? No, because it never stalls.

Can it do aerobatics? Only figures which are possible with quadcopters if the right control sequence has been pre-programmed. Regular model airplanes can fly pre-programmed aerobatic figures on the press of a button for at least a quarter of a century now.

Does it sense gravity? Yes, by filtering the signals from the accelerometers through a low-pass filter. The dominant vector of the filtered acceleration points down.

Can it sense the wind? Only sudden wind changes, but not constant wind. If you add an absolute reference like a GPS receiver, then yes. 

A gyro is a sensor for rotary movements, so it will only sense rotations. It does this with three tiny oscillating structures, orthogonally mounted to each other. A rotation will cause the resulting Coriolis force to move them, affecting their capacitive characteristics, which can be used to measure the turn rate in all three axes.

Accelerometers are needed to measure acceleration, and they also measure gravity. Here again, you will find three tiny, orthogonal structures which are deflected by an acceleration, much like a horizontal beam bends down in Earth's gravity field. Again, capacitive changes are measured and converted to acceleration values in the three axes.

Modern sensors combine both acceleration and turn rate in so-called six-axis sensors (PDF!). They can be run at several Kilohertz, so they take measurements a couple of thousand times per second. This fast rate is needed for the almost instantaneous reaction of virtual reality glasses; the sensors in drones should be happy with a few hundred measurements per second.

A big problem of such miniaturized sensors is their drift: If you only rely on a gyro, you will never be able to tell if the system is truly at rest. If the system is standing still, you can use a 6-axis sensor and take the direction of gravity to remove this drift. But you will still not be able to avoid drift in the rotation around an axis parallel to the gravity vector, plus in a moving system you cannot measure the true direction of gravity, so another sensor is needed which is not affected by movements: A compass. It measures the magnetic field, again in three axes, and can be combined with the first two in 9-axis sensors.

The latest generation of sensors can include an ASIC to run sensor fusion software, so the output is not only digital, but already corrected for drift and presented as quaternions, which are superior for calculating rotations. Also, they include only the two inertial sensors and can act as a sensor hub, so the compass can be placed freely where it is least affected by soft iron effects (PDF!) and is connected via a databus (I²C or SPI).