[Arizona Pro-Photo]

The 5th photo is a resonator. It helps dampen the pulsations created in the airflow on naturally aspirated engines.
It's designed to help keep the intake airflow smooth. Without it and you might get more noise and poorer MPG.

The 4th photo is some kind of sensor, but not knowing where it is located in the system I can only guess it might be a mass airflow sensor that measures the air density relative to air temperature.
If it gets dirty it might cause some problems such as rough idle and bad MPG.

I live on a dirt road and I have never seen that kind of dirt in my air cleaner box.
Are you running without an air filter?

 

[Arizona Pro-Photo]

Image 3 shows the little puffy pads that I removed from mine. After 1 or 2 mudholes, you'll need to clean the innards of your intake system. I got a bunch of mud in mine after just one trip, but then I realized that most of it was due to my inner fender liner missing. After installing a new one, it was a lot better. You may want to inspect yours for holes and/or proper attachment, or consider swapping out to a snorkel.

Mine does not have that puffy padding inside the box.
Might have been removed by the prior owner before I got it.
Do you know what Nissan put it in there for?
Seems like something that will accumulate dirt to me.

As far as the resonators I have read a few articles on them and they do serve a purpose.
Here is one article that states if you remove them it might result in a reduction of horsepower and MPG because the resonator's purpose is to smooth out the airflow in naturally aspirated engines.

Here is a quote from the article:
Pressure Wave Harmonics
Air flowing into your cylinder head's intake port doesn't move in a straight line while the valve is open, then politely stop in its tracks to await another valve opening. When the valve closes, the moving column of air slams into it, then compresses and bounces back like a spring. This pressure wave travels backward at the speed of sound until the intake runner opens up or it hits something, and then it bounces back toward the cylinder. This is the "first harmonic." The pressure wave actually bounces back and forth two or three more times before the intake valve opens again.
Intake Tube Pulses
The resonator in your intake is technically known as a Helmholz resonator, an acoustic device used to control pressure wave harmonics. Air bouncing back out of your engine and into the intake tube doesn't do it in a single pulse the way it would in a single intake runner; the multiple pistons put out pressure waves at their own intervals, and some of those are going to try to bounce back in while others are going out. The result is a "clog" or high pressure area in your intake tube that ultimately limits airflow through almost the entire rpm spectrum.
The Resonator
Adding an expansion chamber to the intake tube forces air coming back out of the engine to slow down to fill the cavity, thus expending a great deal of its energy and slowing the pressure wave reversion. This slowdown allows fresh air to flow toward the engine without fighting pressure reversion waves the entire way, thus aiding in cylinder filling. Since these pressure waves are essentially sound, giving them a place to expend their energy before exiting the air filter box ends up dampening the intake noise and quieting the engine. Thus, the resonator helps to make the engine paradoxically quieter and more powerful.

What Does an Air Intake Resonator Do?

To the average hot-rodder, intake resonators go on the same pile as smog pumps, catalytic converters, exhaust gas recirculation valves and charcoal canisters. But imagine which pile the resonator would end up in if that same customizer knew it was more than a plastic muffler -- it's actually an...

itstillruns.com

To my knowledge they are only for naturally aspirated engines because a supercharger or turbo puts constant pressure on the intake while driving at speed.

 

[Arizona Pro-Photo]

The only reason I can think of for those soft pads is to act as sound absorbers.

Resonators are also used to attenuate the sound of the air movement. Some folks disapprove of any sound from the intake, and apparently the Japanese engineers chose to add 3 resonators and some soft pads to deal with it. The thing is, the pads and 2 of the 3 resonators are on the outside of the air filter. The only resonator between the air filter and intake is the one on the air intake tube, and its ability to do any tuning of the intake runners is limited by the fact that it's not part of the intake plenum or runners, and the effect of the throttle body plate. I would hazard a guess that the butterfly is rarely open 100% of the time, so that will limit any effects of that final resonator.

The way that a number of manufacturers have tuned the lengths of the intake runners (not the plenum, intake tube, or anything beyond the TB) is to have 2 runners for each cylinder. Below about 3ooo RPM, the longer path is available, above 3ooo the shorter path is made available. This is done in a manner similar to when the throttle plate opens and closes. The longer paths are more optimal for lower engine speeds since the sound pressure waves have to travel further, which makes them take more time to return and thereby affect the airflow. The shorter paths are more optimal for higher engine speeds.

It is nice to work on my rig without them in the way, and having taken out the one under the fender means that there are 2 openings for fresh air to reach the filter rather than just one.

That does sound logical that the padding is for sound absorption, but if it does nothing to improve the airflow then I would agree that the padding can go. All it does is trap dirt anyway.
If the resonators are tuned to keep airflow smooth at specific RPM ranges then you could probably get away with removing them and not suffer any performance or MPG problems if you're driving at certain speeds.
However, if I understand you correctly, the resonators are best if you're driving at low speeds most of the time where the air is flowing at a slower rate and therefore more susceptible to pressure rebound in the system.
If that is the case then removing them would be detrimental for MPG and performance with slower city driving.

I guess the only way to know for certain is to experiment.
Do a mileage measurement with them and without them and see which is better.