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The question doesn't say if the pond is stream fed. If it is groundwater fed - it will take much longer to freeze, due to the fact that the groundwater is moving through an insulated body (ground) and continually adds warm water to the system. This will most always be noticeable at an edge of the pond that never freezes over or takes much longer and colder ...

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It is a simple adiabatic scenario. When an air parcel idiabatically raises, its heat exchange with surrounding is zero. Therefore, the decreased internal energy (with the related temperature decrease) of an air parcel is equal to the work done by the parcel during its expansion, and vice versa. This change is reversible.

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The whole idea of well-mixed is that it all has the same properties (as you note the moisture profile, the left line, also follows the mixing ratio, showing it has the same moisture.... winds don't have to be constant, as they are driven by surrounding pressure fields, but will tend to be more similar than in unmixed profiles) Well in terms of temperature, ...

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The thing is, the density decreasing with height, which is caused by the reduced surrounding pressure, does mean the air is spread out more... but likewise also means the water vapor must take up a larger space for the same amount of molecules too. And so that density/pressure change basically doesn't mean any "more room" for water vapor (the ...

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Be aware that vapor capacity in $\pu{g/m^3}$ is property of space and water itself - air is just a spectator here. It grows about exponentially with temperature, typically doubles every $\pu{10^{\circ}C}$. The given absolute humidity in $\pu{g/m^3}$ slightly decreases with temperature ( at the same pressure ) due air thermal dilation. The absolute humidity ...

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