Function and purpose of crankshaft position sensor and two camshaft position sensors?

The crank and cam sensors tell the engine control unit where they are located as the engine is turning. The ECU then controls all of the rest. Unlike older vehicles that used a crank trigger or even the reluctor designs to control timing and such, that is all internal to the ECU in your vehicle. It uses driver transistors for each cylinder to control the spark and fuel by turning the grounds to each one on and off as each cylinder is in operation. The knock sensors entire job is to set there and tell the ECU if there is any detonation from a bad fuel mix or just low-grade fuel, the ECU then adjusts the timing as needed. It is a piezo type sensor and reacts to anything that produces vibrations in its detection range. A quick way to test them is to watch the timing on a scan tool and tap the engine block with a hammer and watch for the timing to change.
As for no TPS, it has two of them. They are inside the throttle body and serve as feedback to the ECU for the throttle plates position, it uses that info along with a virtually identical sensor mounted to the pedal assembly to regulate the airflow into the engine. It does not however regulate fuel flow that is done using the signals from the MAF, coolant temperature and load calculations that the ECU does.
If the O2 fails, it will depend on the failure mode. In most cases the ECU will shift from real time to substituted values and the engine will still run but not correctly and in most cases, it will reduce power. Yours also doesn't use a common O2 sensor but an air fuel ratio lambda sensor. Much more sophisticated than a common sensor that just reads the amount of unused oxygen in the exhaust. They are also not a common failure item, although one of the first things a parts store will say if you get any CEL will be, oh change the O2 sensors.
Doesn't matter what the real issue is. Same thing if you get a P0301 code, "Oh change the plugs and coils" we call it "the parts cannon" as in, load up whatever parts are in that system and change them all. The problem with that approach is that you have a code for a single cylinder misfire, so why would you change 4 coils and 4 plugs without doing some simple testing first. Say you removed the coil from cylinder 1 and swapped it with the coil on cylinder 3, takes about 10 minutes to do. Now you drive it, and the misfire is now P0303.
What does that tell you? Likely a bad coil. At the same time, you could swap the plugs from cylinders 1 and 2. Now when you drive it shows a P0302 instead, that would tell you that the plug is the issue. But you didn't just hand over a few hundred dollars for parts you likely didn't need either, so the parts store is upset.

The reluctor wheels are part of the cams and crank. Others use bolts on parts that have the reluctor wheels on them. But they still don't directly control the ignition. They just tell the ECU where the crankshaft is, so the ECU knows which cylinder is coming up to TDC. The cam sensors tell the ECU what the cams are doing, and which valves are open. The ECU uses the tables that are programmed into it with the various cylinder positions, injector pulse width, ignition timing, engine load and more to fire each cylinder in the proper order and then does the same thing for the next cylinder. Your vehicle is a bit behind the latest bleeding edge tech, but it still is very dependent on the technology to make it work.
If you want to spend some time you could visit YouTube and watch some of the top folks showing the things, you are asking about.
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Sorry for that.
No EGR system like that, it uses the ECU and valve timing to achieve similar results.
Every vehicle made since about 1985 has a charcoal canister and some form of EVAP system. Yes, it has an AC pressure sensor system on it.

I don't like to be the bearer of bad news, but VVT sprockets can stick and cause issues. It's not really common in most imports, but it can happen. These days most engines are buried under covers and have intake blocking access. I think it's one of the reasons why the service intervals for things like plugs keep getting pushed farther back. Mid 80's you did a full tune up every 40-50K, these days that has been pushed out to 100,000 on the plugs, transmission fluid and coolant that are "lifetime" and oil changes that are 10,000 or more.
The mantra is "Oh the lubricants and machine work is so much better that this is normal" The reality is that 99% of it is simply marketing BS. The companies look at the way most people trade vehicles every few years or as soon as the warranty is up and feel that as long as the vehicles make it that far it's all good. Folks like me who keep a vehicle in service for 200,000 or longer are not the normal, so we don't count.

Generally, it won't, but like anything else, there are exceptions. A friend had a BMW that wouldn't start because it had a bad driver's side exterior door handle! I had a GM that the owner had towed in because it wouldn't start, it was because the memory fuse to the radio had failed, and it couldn't match the VIN to the key because the BCM also lost an undocumented power feed on the same fuse. As they get more complex it gets worse. That is why I tell folks new in the field to get into the electronics and diagnostics more. The mechanical part is the easy side now.