I have a 2012 Mini Cooper S Coupe with 55275 miles on it. About a week ago, when starting up the engine started having misfires. I have tried thinking through the problem, capturing frames from my BOSCH Bluetooth connector, and recording videos. I have noted the following behaviors:

- When cold cranking the startup is very rough (most of the misfires happen at this time)
- After an initial rough start the engine has been running relatively smoothly although it has been getting progressively worse each time I drive it locally
- I noticed that the plastic air tube going into the side of the engine below the main air filter (on the driver side) seems to have vibrated into a very loose condition near the back rear (I've tried to use my hand to vibrate it back into place but it doesn't seem tight enough to me)
- I have ordered and received the ignition coils, spark plugs, and oil filter so that I can swap them in after I check the air filter
- I noticed changes in the engine rpm when I change the amount of air that I use for the internal AC
- Noted random codes: P0300, P0301, P0302, P0304, P15DF
- When the car is on the road and stopped at a stop/red light the engine RPM idels at around 700-800RPM. 

**What I have done to prepare for the solution:**

- Watch videos for other people's assessment of these kinds of problems
- Gather basic tools necessary to address fire, air, fuel issues
- Develop a mental picture of the problem and define a plan to address the most obvious potential issues first

I understand that it certainly could turn out to be the high/low pressure fuel pump or a mechanical failure. I would like to know if anyone can offer any insight or tips. I have saved the video of my live data capture over a period of time in the hope that someone can point out anything that I have missed.

Other things I don't know but would likely be helpful:

- How can I adjust (increase) the engine idle RPM?
- What other things I should be doing
- How to adjust spark plugs or at least verify them before installation

[Live Engine Videos / Frame Captures / Live Data Captures][1] 

P.S. My nearest garage is talking about a $250 fee to look at the problem (not fix it) so that is never going to happen.

Thanks in advance for any assistance or recommendations.

  [1]: https://photos.app.goo.gl/S68K3x7oNwFm4c4s9