No, there are high altitude deserts also. An example is the Ladakh with much of it being over 3,000 m (9,800 ft. It extends from the Himalayan to the Kunlun Ranges and includes the upper Indus River valley.
Subtropical Highs
The only thing all deserts have in common is low rainfall.
All deserts have low precipitation and high evaporation rates.
Your question is redundant. All deserts are classified as deserts because of the low precipitation.
Some deserts have low elevation, some have a rather high elevation. Not all deserts have a low altitude.
Low latitude deserts are primarily located near the Tropics of Cancer and Capricorn, roughly between 20° and 30° north and south of the equator. These deserts, such as the Sahara and the Kalahari, are formed due to the descending air of the Hadley cell, which creates high-pressure systems that inhibit cloud formation and precipitation. The intense solar heating in these regions also contributes to high evaporation rates, further limiting moisture availability. As a result, these areas experience arid conditions with low rainfall.
Most of the USA - all of the "Continental US" - is "mid-latitude". The State of Hawaii is "low latitude", while Alaska would be considered "high latitude". The boundaries are subject to some level of interpretation.....
There is no limit by latitude for deserts. The Antarctic Desert is as far south as it could possibly be. The Gobi Desert is also located well north. Many deserts do occur between latitudes 30 and 35 north and south, however.
It depends on your latitude and logitude, and if your in the deserts or mountains, you know.
No, deserts or parts of deserts can be several thousand feet in elevation.
No. Height varies widely. There is even a formal division between high deserts (above 2,000 ft) and low deserts.
The average elevation of the Atacama is 2400 meters or about 7874 feet above sea level.