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.
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.
Every desert has distinct climate statistics. There is not a single answer that fits all deserts. You need to specify a particular location.
The average elevation of the Atacama is 2400 meters or about 7874 feet above sea level.