>What major command is headquartered at Peterson AFB, CO / Cheyenne mountain?
Northcom
>What is NORTHCOM / NORAD's mission?
https://fas.org/sgp/eprint/northcom-opplans.html
>Why have so many very high ranking military and government officials flown in and out of Peterson AFB since January?
What say (You) high ranking officials?
>Who is the commander of NORTHCOM?
GLEN D. VANHERCK, USAF
>Why is this commander so important in a state of national emergency?
From link above: In the wake of 9/11, U.S. Northern Command (NORTHCOM) was established on October 1, 2002 "to provide command and control of Department of Defense (DOD) homeland defense efforts and to coordinate defense support of civil authorities."
>Was NORTHCOM's commander the Director of the Joint Staff immediately beforehand?
https://www.af.mil/About-Us/Biographies/Display/Article/467046/brigadier-general-glen-d-vanherck/
>Does the Director of the Joint Staff advise the President directly?
The Chairman of the Joint Chiefs of Staff is the principal military adviser to the President, Secretary of Defense, and the National Security Council (NSC), however, all JCS members are by law military advisers, and they may respond to a request or voluntarily submit, through the Chairman, advice or opinions to the President, the Secretary of Defense, or NSC.
https://www.jcs.mil/About/
>If the Dir. of the Joint Staff becomes the commander of NORTHCOM immediately afterwards in the month before the foreseen foreign theft of the US presidential election (an act of war) and 3 months before the inauguration, would that be significant?
Could be. Depends on the morals and ethics of person. Time will tell.