Burning smell from PC originating around DVD drive and power button/front usb's.

Take out your ODD and examine all front I/O cables for melted sleeving. You also might want to take off the front I/O frame, so you have better access to the front I/O.

Well, your front I/O has from left to right: power button + it's LED, 2x USB ports, audio and mic port, 2x USB ports, 1x unknown port (looks like HDMI port) and 1x button (probably reset button). How many of those you have connected, that i don't know.

As far as power goes, there is a current inside the audio and mic ports too. I have several such speakers and mics that draw all their needed power from the audio/mic ports.

When was the last time you cleaned your case internals from dust? Since i see quite a bit of dust on your pics. As far as the smell goes, one possibility is that it's the dust that burns inside your PC and the smell is carried upwards with hot air (since hot air rises) and if you have positive pressure inside your case, the hot air along with the smell is pushed out from any of the small openings at the top of your case, including front I/O area.

Though, the front I/O cables look intact without any burn marks and i can't tell from where the smell could originate (besides burning dust). If the dust cleaning doesn't help then to be safe, i suggest you should replace the PC case. New PC cases start from $25,
pcpp: https://pcpartpicker.com/products/case/#sort=price&p=0&u=1&f=2

I don't know what that "black box" can be but according to the images, it's just behind that last button in the row that i first thought to be a reset button. Without knowing your case make and model, i can't say what that could be. It could be a fan controller for all i know.

Do your case also has hot-swap bay? Since i see wires going there and there's also an opening on top of your case. That smell can originate from there as well since hot-swap bays are connected to the PSU for their normal operation.

Fun fact: My Skylake build (full specs with pics in my sig) has the very same ODD as you have. At least the front exterior part is identical by looks.

Wow, you have an old timer from Corsair in use. I too have Corsair Obsidian case where my Haswell build sits in but mine is 750D Airflow Edition (full-tower ATX).

Since now i have access to the case specs, that last button in row on your front I/O (round one) is the reset button. Also, your case does have hot-swap bay at the top of the case as i suspected. Hot-swap bay is mainly used for external drives to back up data. And we also know now what that magical "black box" is in your front I/O. It's the fan controller unit.
650D fan controller spare part: http://www.corsair.com/en-us/obsidian-series-650d-fan-controller-kit

When looking your images, i thought that the fan controller switch is actually a clip that holds the foldable front I/O cover in place since my 760T also has two of such clips to hold the front grille in place.

Did read from the net that many people have issues with the 650D built-in fan controller. Since fan controller is connected to the PSU and there's a small PCB inside that "black box", it very well may be the source of your burning smell. Unplugging fan controller from PSU would left it inert but all the case fans that are connected to it won't work either.

As far as new PC case goes, you can either go for the one that also has built-in fan controller (e.g Corsair 760T v2 or 780T) or which doesn't have one while having more-or-less the same looks as your current case (Corsair 450D and 750D). Even when the case does come with built-in fan controller, you don't have to use it and left it unplugged, like i did with my Skylake build's 760T v2.
Since i don't know your taste about PC cases, i can't suggest you one but Corsair and Phanteks PC cases have solid build quality. NZXT cases are also popular nowadays.
Corsair lineup: http://www.corsair.com/en-eu/pc-computer-cases
Phanteks Enthoo lineup: http://www.phanteks.com/Enthoo-Series.html
Phanteks Eclipse lineup: http://www.phanteks.com/Eclipse-Series.html
NZXT lineup: https://www.nzxt.com/categories/cases

Yes, your amazon link shows different kinds of fan controllers, both internal (e.g Silverstone) and external (e.g NZXT Sentry 3). I prefer using external fan controllers that sit in the 5.25" bay since with them, i have more control over my fans and they also provide some eyecandy. And thanks to this, all my 3 PCs: Skylake, Haswell and AMD have external 5.25" bay fan controllers (full specs with pics in my sig).

Internal fan controllers are handy if your case doesn't have external 5.25" bay or if you don't want to see the fan controller. Though, most internal fan controllers are more like fan splitters than controllers since you can't control individual fan and they all run in sync (e.g Silverstone). Only those internal fan controllers that have dedicated software to control them have control over each fan separately (e.g NZXT GRID+ V3 and Corsair Commander Pro).

While all external fan controllers have dedicated channels for each fan and you can manually control the speed of each fan. Many external fan controllers also come with temperature sensors that you can spread all over your case to see the internal temps of different components. Also, some external fan controllers have LED touchscreen if you like it more than knobs/switches (e.g NZXT Sentry 3 that i have in my Haswell build). And some external fan controllers even have support for LED strips (e.g Thermaltake Commander F6 RGB that i have in my Skylake build). Of course, you need to read the external fan controller specs (and review) before getting one since some may come with different view angle. E.g Aerocool X-Vision that i have in my AMD build is designed for PCs that sit below your eye level, making it easier to read their info from above, rather than straight on.

When i was looking for a fan controller for my Skylake build, i made a topic where i listed many fan controllers with links to the specs. You can use my topic as a source for the specs of different fan controllers. It's better than searching fan controllers from amazon,
link to my topic: http://www.tomshardware.co.uk/answers/id-3380313/led-fan-controller-external-bay.html

So, you checked out my Skylake build and saw that i have 7 case fans in use (mostly 140mm) and thought that my PC should be noisy due to having so many case fans, right? Wrong.

The trick is that the more fans you have inside the case, the less each fan has to work to maintain the airflow and the less noise fans produce. Also, 140mm fan movers more air than 120mm fan at the same RPM. And that is also a main reason why i have 7 case fans in my Skylake and Haswell builds. Since i have that many case fans, i can keep all of my case fans spinning between 800 - 1100 RPM and thanks to this, my PCs are very quiet while still having proper airflow inside my full-tower ATX cases.
Of course, i'm using high airflow and high static pressure fans inside my PCs since even when they spin at about 50% of their max speed, they still provide good airflow.

If i sit still and do nothing then i can barely hear my fans working but the sound they produce is low and calming. If i'm working on something or listening some music, i can't hear my case fans at all. Closest sound example to my fans is this river flowing sound but my fans are much quieter than that sound in the video,
youtube: https://www.youtube.com/watch?v=eRFzN_x_pww

NZXT Sentry 3 is standalone fan controller and there's no need to use your built-in fan controller anymore. You can completely disconnect all wires coming and going from it.

200mm fans, at most, spin about 800 RPM or so and they are quieter than 120mm and 140mm fans (max RPM usually 1500-2000). Though, for cooling aspect, 2x 120mm fans do move more air than 1x 200mm fan.

What make and model (or part number) PSU do you have?
I had a low quality Codegen PSU who's fan also started screeching. Got tired of it and i threw it out and bought Seasonic S12II-520 to replace it. I still have my S12II-520 in service (about 3 years now) and it's still going strong while powering my AMD build.

While i5-2500K was solid CPU at it's time, it does show it's age, especially in CPU bound tasks. Cities: Skylines is very CPU heavy game and your CPU can struggle with it quite a bit.

As far as Ryzen vs Intel 8th gen goes, Ryzen CPUs are better in multi-core performance (e.g video rendering) while Intel 8th gen are better in single-core performance (e.g web browsing) and quad-core performance (e.g gaming),
Ryzen 5 1600X vs i5-8600K: http://cpu.userbenchmark.com/Compare/AMD-Ryzen-5-1600X-vs-Intel-Core-i5-8600K/3920vs3941

If you mostly do productivity work, then go with Ryzen CPU. But if you mostly game then go with Intel 8th gen CPU.

Oh, listening loud PC all the time can give you headaches and it will reduce your hearing. So, i don't suggest getting a similar or same as Noctua industrial fan (which does have superb cooling performance) that you can run 24/7 at max RPM. 41.3 dB(A) is way too loud to listen all day long.

There are 3 different versions of Corsair TX 650 PSU and here you need to look the part number on the PSU's label:
1. CMPSU-650TX-C
2. CMPSU-650TX
3. CMPSU-650TXV2

1st one is made by Channel Well Technology and since CWT being 2nd grade PSU OEM, i'd say the PSU has mediocre build quality.
2nd and 3rd ones are made by Seasonic and Seasonic is 1st grade PSU OEM. Every Seasonic unit is solid as a rock and so far, Seasonic has never produced anything lower from good quality units over the past 40 years they have been in business.

Corsair TX 650 had 5 years of warranty and if you're running Seasonic unit, then you can get up to 10 years of usage out of it (even maybe more). Though, i'm not so sure about the CWT made unit.

For your PC usage, Intel 8th gen CPU would be better since the drawing you do doesn't use multi-core performance in which Ryzen CPUs are best.