I took my 2003 XG in for service recently because is of a 'moaning' which worsened when the car was turned. They told me that the powersteeringhose had to be replaced ($700+). Well, the noise returned less than 10 days later, accompanied by a brand new leak underneath the car (not transmission fluid or oil).
It seems to come from the right front side of the engine and increases in volume when car speed increases and is really bad when making a turn. It's a whiney/moaning sound
Additionally, there is a secondary noise that seems to come from behind the left side of the dash and can only be described as a crackly noise, sort of like leaves crunching or what you moight imagine electrical snapping might be. It is accompanied by another sound, almost like it is 'breathing'.
I know my descriptions are not great - anyone have any ideas what these might be? The dealership does not seem to have a handle on this and I'm already out $700+ which is discouraging.

 

First of all, your problem is not related to the fuel pump.

While the part is expensive, I think $700 for a pressure hose replacement is high. Once you resolve this matter, I'd find another dealership for service and ask for estimates.

The power steering is leaking to the point that the pump is running dry, hence the whinning noise. Unfortunately, Hyundai uses a proprietary power steering fluid that is only sold by Hyundai and Kia dealerships and is not comaptable with other fluids including the so called "Universal" fluids. You need to buy a quart of Hyundai PSF3 fluid to fill up the system. Take the car back to the dealership that changed the hose. Do not be surprised when they say the pump had been damaged before you brought it in for the hose repair.

I think XG350s and Azeras have a reputation for noisy ABS pumps in the brake system. The steering rack is also mounted just in front of the firewall. If the rack is totally out of power steering fluid, it too would make strange (and potentially dangerous) noises. You might open the hood and try to better locate the noise while the engine is running.