Temperature
Here we are clearly interested in the temperature at the height we live in. Placing it too close to the ground would create a significant bias. 2m is about the max that is reachable for a human without a ladder or some stairs.
You are right in that the surface can have an effect, but the surface below the station is also described in quite some detail so at a professional station this will not be a problem.
Absolute ideal situation (usually the case of pro-stations at airports)
The site is covered with short grass (height ≥ 4cm and ≤ 10cm). The area will need to be mown at least once a week in the period from April to September, meaning it will be mown about 28 times in the grass growing season. No crops or plants exceeding 0.5 m in height may be grown or placed within a radius of 25 metres around the observation site. No crops or plants exceeding 1.5 m in height may be grown or placed within a radius of 50 metres around the observation site. No obstacles such as trees and shrubs may be placed within a radius of 100 metres around the observation site. No obstacles such as sheds or other buildings and woodland may be placed within a radius of 400 metres around the observation site.
The sensors for measuring temperature should according to the WMO be situated at a height of between 1.25 and 2.00 metres above flat ground. The terrain above which the measurements are being made should be covered with short mown grass; any snow that may be present need not be removed. The measuring element may not be significantly affected by sunlight, radiation and meteorological phenomena such as precipitation, dew, frost and wind. For this reason, the measuring element is placed in a so-called “dish screen” (shaped like an inverted dish) that protects it against radiation. This casing is white on the outside and black on the inside, to minimize the influence of radiation. The space between the dishes is chosen so that sunlight and radiant heat have no effect on the measuring element and also so that the space inside the screen is suitably naturally ventilated.
Wind
Theoretically yes, you could measure it close to the ground, however this would require an absolutely open space with no obstacles and nothing that could create a bias on the actual ground. This in practice is close to impossible. For this reason it is measured at 10m height where it is not affected so much by obstacles and turbulences near the ground. Also for the planes at the airport the 10m height is more relevant.
The sensors for measurement of wind speed and direction are mounted on a stable metal or plastic mast. The sensor height is 10 metres above terrain that should in principle be flat. The distance from the wind mast to any obstacles in the vicinity must be at least ten times and preferably twenty times the height of the obstacle (applies to all obstacles).
The terrain in the immediate vicinity of the wind mast (radius ≥ 100 metres around the measurement site) is flat grassland or a water surface. The wind observation at an airport must be representative for the wind conditions on the (adjacent) runways for take-off or landing, and in particular for the touchdown zone.
Conclusion:
Most of us will never have a perfect station so no need to worry about it too much