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How high in the atmosphere may an air-current form? Can a wind current form up in the mesosphere?

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Certainly. Any time there is a temperature gradient, air will move. Altitude doesn't matter (from the standpoint of existence, the speeds possible are different based on air density).

Numerous papers investigate both what causes winds in the mesosphere as well as what effects these winds have on various atmospheric formations.

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In the stratosphere and mesosphere, temperature follows the radiative equilibrium such that you have high temperatures due to absorbption of solar radiation by ozone at the summer pole whereas the region above the winterpole is cooler due to the lack of solar insolation (polar night). According to the thermal wind balance this leads to easterly winds in the sommer stratospher / thermosphere and westerly winds at the winter stratosphere / mesosphere.

At the mesopause (about 80-85km) during the solstices the wind is reversed in both hemispheres due to the by upward propagating gravity waves driven residual summer to winter pole circulation. In accordance with this circulation, the upwelling at the mesopause leads to a very cold (colder than it would be in radiative equilibrium) sommer mesopause by adiabatic cooling, and a warm (warmer than in a hypothetical radiative equilibrium) winter mesospause. According to the thermal wind balance again, these dynamically induced temperature anomalies are accompanied by a reversel to westerlies at and above the cold summer mesopause and to easterlies at and above the warm winter mesospause.

The interaction between atmospheric waves and the mean flow which is relevant not only in the middle atmosphere but in the troposphere lower stratosphere, where it drives the Brewer-Dobson circulation, is mathematically described by the TEM (Transformed Eulerian Mean) equations.

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