Is it permissible for someone who performed Hajj Mutamatti' and was delayed from spending the night in Mina on the Day of Sacrifice due to traffic congestion to spend the night there at 1:00 AM on the following day?

The madhhab of the majority of scholars is that the obligatory overnight stay in Mina, for both those who hasten and those who delay, is only fulfilled by spending most of the night there. The details are as follows: Malikis: Whoever misses most of the night in Mina owes a dam (sacrificial animal), and likewise if they miss an entire night or more. Shafi'is and Hanbalis: Whoever misses most of the night in Mina owes a mudd of food for each night. If they miss the overnight stay for all the nights of Tashreeq, they owe a dam. This ruling applies to those who are not excused; as for the excused, they owe nothing.

The preponderant opinion is that of the Shafi'is and Hanbalis. Based on this, you owe nothing because you did not neglect your duty and you did what was within your capacity.