What are the rules for running nitrous lines inside the car? I.e., running the feed line from the bottle inside the car and installing a mechanical nitrous pressure gauge inside.

I have the 2003 NHRA rulebook, it doesn't mention anything about it besides the blowdown tube.

 

There isn't any rule. The pressure blow off line must be vented to the outside but the nitrous line can go anywhere you want. Nitrous isn't a fuel. It's an oxidizer.