I completely understand the whole helping part.
But bad gas mileage can be the cause of just poor maintence too, maybe a tune up is in order from them aswell. Though the rotten egg smell is a tall tale sign of a bad cat.
As for you intake noise, thats completely normal, is the rushing air past the IAC valve and just motor noise that a regular muffled stock intake wont let you hear. And loud exhaust while gaining speed, I would look at maybe an exhaust leak at the resonator and maybe over time the mufflers start to rot out on the inside a little.
