距 is short form for 距離 (distance from)
you can replace 距 with 距离 in all the examples you listed.
You can also replace 距 with 离 in all the examples above.
距 is more literary and 离 is more colloquial
However, they are used when expressing distances, doesn’t matter whether vertical or horizontal, you can use either of these three words
Furthermore, 距离 literally means "Away from". It can be used to describe 'distance from' like all the examples mentioned in the question, and it can also be used to describe 'time till' For example: "距离东京奥运尚有854天" (still 854 days away from Tokyo Olympics = Time till Tokyo Olympics is 854 days)
"离东京奥运尚有854天" is also correct
"距东京奥运尚有854天" is not incorrect, but sounds too literal and formal