04 Mustang engine flutter?

My son's 04 Mustang 3.8L V-6 is making a fairly loud fluttering noise comparable to an exhaust leak, which I had thought it was.
Upon starting cold, it really makes some noise, I checked the exhaust system and when the engine was started, I followed the noise to the engine itself, up to somewhere around the a/c compressor (was energized/clutch locked on)then as the engine ran the noise got progressively quieter to the point of very little/none. Could it be something with the air emissions equipment. I don't think there is an air pump on this late model car but that is what I would think it was other than the exhaust leak that I was hunting.
One other oddity is there is a section of black fuel/gas hose near the automatic trans. dipstick that is deteriorating badly, very chalky(black residue), the hose goes into the fuel throttle body right behind the what looks like a TPS or other sensor on the air intake body. The hose is marked fuel/gas hose, I would like to replace it soon due to the deterioration. If it carries gasoline it could split/rupture. Also, I see the bad hose section connects to another hose section with a plastic type coupling/union. Can somebody explain what hose this is, could it be a fuel return line? And can it be replaced easily?
Thanks guys, always needing your great assistance,

Response:
check your Cat for a tube coming off the side, follow that tube if not capped off at the cat, to a diaphram valve assy. where it connects to a rubber hose. I think you'll see the problem.
Now the fuel line could be either pressure or return and they are braided which is why there's a union. There are 2 types, 1 uses a special tool like A/C unions. The other has a plastic clip that usually breaks and cost $.15 from most Parts Outlets. But they generally run up the frame rails away from the trans.