Codes P0302, p018, PO108 and PO113?

Watch the data PID FRP(kPa) when you turn the vehicle off. Turn the key right back to On, engine Off and watch that data PID, that's the Fuel Rail Pressure data, if it drops off quickly then an injector might be leaking, but the MAP sensor reading of 255kPa is too high, does that change if you push on the gas pedal when idling in Park? It should go much lower.
Can you change the scan tool setting also so the FRP is reading in psi and not kPa? But really you need to monitor that 4210kPa data PID, if it does drop off with the key On, engine Off, then it may not be an injector, check that first. And if you're changing GDI injectors make sure you pull the fuel pump relay for the pump in the gas tank and relieve the pressure first before cracking the high-pressure lines open. There's 1000s of pounds of pressure there, and you can get hurt very easily.

So, the MAP is no longer setting any codes? Or you haven't gotten to that yet? It's difficult with a MAP reading in kPa, instead of either psi or inHg. But I believe a MAP should read around 27 kPa at idle if I have that correct. But that will also vary depending on where you live, higher or lower than sea level, since the MAP reads absolute pressure. The Fuel Rail Pressure test is a good test when dealing with GDI systems, since you can't just tap into the fuel rail like a conventional system and do an injector leak down test, you probably could with a more advanced scan tool, but not a basic global OBD2 one. The PCM may have stopped reading data from the MAP since it was so far off, but the Fuel System status should go to CL Closed Loop now when it gets to operating temperature, and that OL Fault should disappear.
One other thing is change your oil ASAP, if the fuel issue is taken care of and no more smoke, the oil is highly contaminated with gas now, so change that and the filter before you drive much.
Hopefully the Catalytic Converter didn't melt down during all this, you will get a p0420 if that's the case.

Yeah, the rear 02 should stay pretty steady, around 0.6-0.7v roughly, I'm not sure how difficult it is to get to the spark plugs on this engine, but if the #2 is leaking down that fast, that cylinder will be flooded with gas. Another check you can do, after the engine is off and the pressure leaks down, if you can pull the #2 plug out, disable fuel by pulling the fuel pump relay or fuse, unplugging the injectors, or the vehicle might have Clear Flood mode if you hold the gas pedal down to the floor and crank, some will disable injectors during clear flood mode. Then put a rag over the open spark plug hole and crank it, see if a ton of gas comes out of the cylinder. That much fuel in the cylinder is going to lower compression as well due to cylinder wash.
I'd be curious to see how it runs with the MAP sensor unplugged. Since I don't see a MAF sensor, some systems will default to known good data when some components fail like this. I don't know if it would do that for a sensor or not, sometimes on GM vehicles it will for failed modules. Here's the OEM injector part number if needed. How is the #2 coil doing, not over heating at all?

If you own a bore scope you could pull the spark plug and look into the cylinder that way, it's a great tool to verify all kinds of diags, I use it sometimes just to take a look at intake and exhaust valves, cylinder wall condition, catalytic converters, etc. Its worth every penny if you're going to keep doing your own repairs. With a bore scope in the cylinder, you should be able to look right at the tip of the injector and see it dripping fuel.

No that's not normal, with 2 intake valves and 2 exhaust valves, each pair should be the same. Are you taking a video with the valve cover off?

If the valve cover is off, you can take a look at the valve springs and see if one is broken, take a picture if you can't upload a video. Is it the #4 that you see a valve hanging open?
The valves are adjustable on this engine, but it's with tappets that sit under the camshaft lobes, and wouldn't cause the valve to be open enough to visually see it.

It's difficult to see in the video, but I'll take your word for it, did you pull the valve cover off and inspect the valve train for any issues? They're very clean for being a GDI system, usually there's a ton of carbon build up on the valves and it requires a walnut blasting to clean them out. But I would start by checking under the valve cover to see if there's anything you can spot visually. Thats definitely going to be the cause of the #2 misfire code. Obviously if you find a broken valve spring, it will have to be replaced. When you have the valve cover off rotate the engine by hand and watch the #2's valve/camshaft movements. But you have a very good idea of what you're doing, I'm sure you can get this figured out. Let me know if you need any further service info.