Right under side of 04 g35 coupe.

What part Number is this should I be worried, no leaks but I do have rough idle nd breaks problems.

 

I'm going to guess here as i don't feel like pulling up the FSM at the moment,

But fuel and brake lines. Looks like crush damage to at least two of them.


EDIT: looked through the FSM. They don't show line routing, but my guess is more than likely accurate. 2 fuel lines (feed and return) and 2 brake lines for each caliper out back.

 

The smaller lines should be your break lines. You need to get that fixed, definitely a problem. It was also explain your brake problems as you might have lost fluid. Is your reservoir for the brake fluid low/empty?does the peddle feel really soft and not want to stop the car? Definitely not safe to drive with no rear brakes.