Ah, something that has been long overdue.
Assalam-O-Alaikum,
For everyone following this thread and looking for solutions to this problem, I'm sorry for not updating, happenstance has not allowed it. Finally, an update that has been long overdue and I believe a lot of you would want to hear. I did, get rid of the CEL, Alhumdulillah. It's been almost a month now, but as I had thought, it happened when I completely gave up on it and was not looking to fix it.
Here's a picture of the current km count, its been almost 600km. Getting rid of the CEL was actually a series of events, performed in the right order, that I could've never opted for individually unless needed. What I'm trying to say is, it all happened cause of luck. Now the major part, how did it happen?
Last I left this thread at giving up, I had already done a list of things, wiring checked, vacuum lines, fuel pressure, multiple sensor checks, fuses, fuel cap etc., the list goes on. Some of those things I do believe played a part in fixing the CEL with the code P0130. I think this error code is too general in a sense cause the O2 sensor can be affected by a myriad of things, and car manufactures should add more specific codes, would help a lot, nevertheless onwards to the solution.
3 Things done after all the previous things I had already done made the CEL go away,
Apparently, the most major problem, was the CAT. From the point of view of the O2 Sensors socket, it looked fine. But, eventually, I had it taken out to get it cleaned in case that might work, to my surprise, it was only visible after the CAT was taken out that it was completely BUSTED. Choked from all the sides, and a molted mess from the center, the only part actually normal was the part visible from the O2 sensor socket 
What luck, eh? Not having the budget for a new CAT at the time, I chose to get it emptied, and voilà! The car was perfect, the mileage shot up from 9km/l to 15-16km/l I was so dang impressed, I thought this was the problem. The car was perfect, except the CEL still came on, with the same code. I thought maybe it's cause the CAT is empty so the computer isn't receiving the proper signals. One thing I did, after emptying the CAT was replacing the new primary O2 sensor( the one I ordered) with the old genuine one, thinking that now the problem is solved so no need for this one, I should replace it with the original. I couldn't care less about the CEL at this point since the car was perfect, great fuel economy, acceleration and everything.
The above perfection was short lived, as the car wasn't completely perfect, the drive became worse and worse, because I had never driven this car in a perfect state, the relief it got from fixing the CAT felt great and I thought this is how it's supposed to be, but nope. A lot more greatness was in store for this car, apparently the car began missing and jerking a lot. So, I figured it's about time to change the spark plugs, keep in mind this car had the original factory spark plugs still installed, like damn being a Pakistani "jitna chalra hai chalatay jao" Khair, I got new Irdium spark plugs (Kinda expensive, 1k per plug). Those fixed the missing problem, and when the car drove it was a lot smoother. But, it still jerked, a lot on slower speeds. Keep in mind the CEL was on all this time, no changes in the CEL, assuming it was cause of no CAT I didn't even think about it.
The third thing, as time passed the jerking didn't fix and I got kinda worried, cause it was unexplainable, didn't have the heart to go to a mechanic or anything and explain to them the whole ordeal of the mysterious CEL, so one fine night I thought, hey may be it's that original O2 sensor that's messing up, I had to control my get-go instincts on this as anyone following this thread might know it isn't the first time I felt this, and it never was it. Either way, I did it, just for a test trial phase cause I couldn't think of anything else to be the cause of the jerking and just pretty rough drive. After changing the primary O2 sensor to the new one (ordered online, link provided in some above post) I drove the car for like a week. Trust me, when I say, I have absolutely never driven a car to be this smooth and comfortable, especially this car. Damn, seriously it was a whole world of wonder, a week passed, then another, then another, one day I noticed, no CEL? Woah. That was it.
Apparently, you don't need a CAT, the car doesn't display any CEL without it. The car has been ever so perfect ever since, it's been a month. I get 15-16km/l on AC in the city, the acceleration, the drive, the overall smoothness and comfort is immaculate, I would 10/10 recommend buying a Japanese Swift over the likes of Vitz or Passo. It's a 1.3l(94Bhp) powerhouse when you floor it, with the economy of a 660cc Kei car thanks to the K12B, the CVT is incredibly smooth, and having the safety, comfort and reliability of a Japanese car is unmatched (if you find a good one).
That was all, thank you everyone for contributing to this thread and helping me out along the way. Case closed. I'm open to questions, and offering advice. Jazak-Allah
Japanese Swift 10/10 
