Was India's 46 all out the lowest Test total by a team at home?
And has a team made more than ten times their first-innings total in the second like India did?

South Africa rolled New Zealand for 45 in just 184 balls in 2013 • Getty Images
The sensational start to the first Test in Bengaluru last week saw New Zealand pass India's 46 all out in 43.3 overs (261 balls).
India's excellent comeback in the first Test against New Zealand in Bengaluru last week was only the second time a team had made more than ten times their score from the other innings (considering completed innings only). The only bigger difference came at Edgbaston in 1924, when South Africa were bowled out for 30 in their first innings, but recovered to make 390 in the second, 13 times as many. They still lost by an innings, as England had scored 438.
India's remarkable collapse to 46 all out against New Zealand in Bengaluru was the joint 18th-lowest Test total of all (England also made 46 against West Indies in Port-of-Spain in March 1994).
I think this question was sent, rather optimistically, in the middle of India's excellent comeback against New Zealand in Bengaluru last week. If India had ended up winning, they wouldn't quite have broken this particular record: England beat Australia in Sydney in January 1887 despite being bowled out for 45 in their first innings.
You're right that Joe Root made his highest score (so far!) in his 147th Test, with 262 against Pakistan in Multan earlier this month. The only man to make his highest score later than that is the South African Jacques Kallis, whose best of 224 came in his 150th Test, against Sri Lanka in Cape Town in January 2012.
Steven Lynch is the editor of the updated edition of Wisden on the Ashes