You ever been at a stop light and heard a thumping beat coming from the kids car, 4 cars ahead or behind you, the sub-woofer beat, you can't hear the song, just the beat, the Low Frequency sound.
That's the loudness of any sound, low frequency sound waves travel long distances, higher frequencies die off fairly fast.
To quiet exhaust sound the very first thing muffler makers do is to kill the low frequencies as much as possible, which is not easy to do, but that cuts the loudness by at least 60%, which is the whole point of a muffler, otherwise they would have called it a "louder" instead of a muffler
Headers are about performance, stock 2.9l exhaust manifold is tuned(yes tuned) to create highest negative pressure at the exhaust valves in the mid RPM range.
Most after market headers are tuned to get highest negative pressure in the low RPM range.
Racing headers are tuned to get highest negative pressure in the higher RPM range.
This effect is call scavenging, it uses the velocity of the exhaust exiting one cylinder to lower the pressure on the other cylinders on that bank.
It is a science, the tuning, this is also where the "back pressure" Myth comes from.
DIYers would remove factory exhaust manifolds and install larger pipes(free flowing), then go for a drive, "What the F#uck, I LOST POWER!!!"
Engine must need "back pressure", nope.
What they did was to eliminate the power they were getting from the negative, scavenged, pressure, so lost power.
Free flowing is good for Beer, bad for headers, lol
The negative pressure reduces the load on the engine to push the exhaust out, the negative pressure helps pull the exhaust out.
Headers don't add power(assuming original exhaust is tuned), but they are very effective in moving when you get the best power in the RPM range.
And headers won't, for the most part, effect the sound of the engines exhaust.
And as long as you use the same size or larger pipe to connect to the header you won't effect its performance
Cats are required to be legal, period.
But going with larger diameter pipe size can keep the low frequency sound.
And taking a tip from the old Pipe Organs, large diameter, long and straight pipes make for low notes(sound), bends reduce the low frequencies.