Inside a cloud, the plane flies in a medium (air + water droplets) with a higher density than 'normal' air. If airspeed and AoA are the same, lift should be higher. It is really so...?
No, higher humidity air is less dense than lower humidity air. This is because water molecules are lighter than the nitrogen and oxygen they would replace in an airmass.
any water vapor that gets added replaces either nitrogen or oxygen in our free-moving air. Nitrogen and oxygen make up the majority of our atmosphere, and they're displaced -- or evaporated -- when water takes their place in the air. And water vapor molecules are lighter than both nitrogen and oxygen. In other words, humid air is going to have less heavy nitrogen and oxygen -- and lighter hydrogen and oxygen -- in its place. Remember that they have the same number of molecules, but the air with water vapor is simply less dense
Humidity, therefore, is also an important factor in density altitude calculations.
If we consider droplets "floating" in the air, they should hit the wings at the angle of attack and provide some lift. As they are more dense than the air, the lift should be more that just hitting the amount of air that could substitute the droplets.
There are also other effects like humid air is less dense and if the droplets are large enough to fall they should hit horizontal surfaces, pushing down. The overall effect depends on all these factors and may be complex to define.
No, or at least not lift due to the airfoil (see below). The difference between the air inside of a cloud and that directly adjoining it will be relatively small. Also, the air inside a cloud is less dense in most cases than the surrounding air because it is warmer. The following diagram illustrates the effect:
The air outside the cloud is cooler and more dense. The air inside of a cloud, therefore rises, and outside of it, the air sinks. Any glider pilot experiences when passing beneath a cloud: the glider rises as it travels under the cloud, but as soon as it exits the area under the cloud, the glider sinks.
An aircraft will experience lift inside of a cloud, but this is due to rising thermal air currents, not lift granted by the wing's airfoil.