There is a 3ds Homebrew program that loads .nds files from an sd card instead of a game card. Is this allowed for runs?

We don't have any formal rules on pirated copies of the game but generally it's preferred that games are run on original cartridges when possible.

If you can provide any evidence that UTK2 running on Twilight Menu has no obvious differences to original version, we can consider it. Just some footage of loading up a chapter and doing some of the later, more intensive operations (like Sige or Aletheia) would be a good starting point.