In Test cricket what is the maximum number of runs that can be scored in one over of legitimate deliveries? How many times has this feat been achieved in Test cricket?

The most runs that can be scored off an over (six balls) is 36, by hitting a six off each ball (no byes, wides, no balls etc etc). It has never happened in a Test match. The highest achieved is 28 runs, which has happened twice:

28 runs by Brian Lara (466444) West Indies v South Africa Johannesburg 2003-04.
28 runs by George Bailey (462466) Australia v England Perth 2013-14.
https://www.espncricinfo.com/records/most-runs-off-one-over-233006
https://stats.acscricket.com/Records/Test/Overall/Bowling/Most_Runs_Conceded_off_Over.html

Jasprit Bumrah scored 35 off an over for India v England in 2002, but it was more than six balls (4w4nb644461).
https://www.livemint.com/news/india/jasprit-bumrah-breaks-world-record-stuart-broad-concedes-35-runs-in-an-over-11656762474607.html