1. Is the after market stator/rectifier throwing off some of the electric components in the computer?
The stator isn't turning while the engine is not running, so it's basically an assemby of magnets. Barring any strange failures, it shouldn't have any effect on the electrical system. The rectifier isn't receiving power from the stator, so the only effect it could have on the electrics, is blowing fuses or draining the battery if it had failed with a short to ground. It seems unlikely that any of the two is related with your code.
2. Did I stupidly miss a wire connection or a hose of some sort?
The service manual mentions (see page 4-38), both the conditions under which a C13 is thrown, as well as troubleshooting procedures. There's only one couple connecting the sensor to the electrical system of the bike, so I don't see how you could've missed something, but there might be some wiring problem causing this. As far as hoses are concerned, a disconnected hose exposes the sensor to ambient pressure, which is pretty much what happens when you twist the throttle wide open. I wouldn't expect it to throw a code, but the manual does mention leaks and clogged hoses as possible causes, so in any case, you'll have to investigate.
3. I did remember I touched the top most intake flap out of curiosity (Forgot what it was called) and it moved slightly, did that trigger a sensor to malfunction?
No, but note that the secondary throttle valves are servo-operated. Since servo geartrains are designed for the maximum torque that the motor can transmit through them, operating them manually, like you did, can easily applie back-torques that exceed the design limits and strip gears, or break shafts. Therefore, it should be avoided, or, if necessary (such as when performing certain maintenance tasks on the throttle bodies), one should be very gentle in handling them.
4. Is the oil light on because of the code, and if not, what should I do about that? (I put in about 2.8 qts while checking the window on the side, and when I first put the oil in I warmed it up and checked again and topped it off so I don't know if maybe I did put too much or too little in there).
The "oil light" is actually a general "fault indicator", and may light for several reasons. If it's on because of the oil pressure, it'll be accompanied by an oiler icon on the dash (Note that that's only a problem when the engine is running, since if not, there's zero pressure and it should be on). It will also light when a code is thrown though.
In any case, if in doubt about the oil quantity, it should be checked as described in the service manual. (Put on level surface, operate engine for a few minutes, let it sit for a couple more and check sight glass.)
5. I washed the K&N with soap and water (Probably should've bought the cleaning kit) and let it dry overnight, maybe its detecting moisture in there and doesn't like it?
I doubt it, though perhaps some of the oil, moisture and or loose debris in the filter might have clogged the sensor or vacuum hoses. A long shot, but I mention it, since you brought it up. I'd advise ditching the aftermarket filter in favor of OEM in any case.