Is a tornado a meteorology?
There is no such thing as "a meteorology". Meterology is the scientific study of weather. A tornado is a weather event.
It is unclear what is meant by this questions. Tornadoes fall pretty clearly into the field of meteorology. If you are asking about a tornado that does not occur on a plain or a field; tornadoes are not significantly affected by small surface features. A tornado can go over trees, buildings, hills, and mountains without being significantly affected.
According to the glossary of meteorology a tornado is defined as "a violently rotating column of air, pendant from a cumuliform cloud or underneath a cumuliform cloud, and often (but not always) visible as a funnel cloud." In meteorological terms the vortex described above must connect to both the ground and the cloud base to be considered a tornado.
In meteorological terms, no. Though they may be considered large by human standards. The average tornado is 50 yards (150 feet) wide. Tornadoes under 10 yards occurs as well. Some tornadoes can be over a mile wide, but this is still considered microscale in meteorology. The largest tornado ever recorded was 2.6 miles wide.
I am a meteorologist who, in addition to other schools, attended the Air Force meteorology school in Biloxi, MS. Air Force meteorology focuses more on aviation weather instead of surface-based meteorology. Meaning on how weather will affect aviation/mission readiness/mission outcomes/how to prepare for flight etc - whereas regular meteorology looks at surface-based meteorology, meaning how will the weather affect ground-based populations etc.