So I cleaned the battery connections a little, and the car seemed to start up upon first go this time.

After letting the car sit for a couple hours, I retested the battery and got slightly better voltages:

~12.5V with engine OFF
~14.10V with engine ON

I took the car for a drive but I still get the choking response after driving it for a while, and when attempting to accelerate quick the car chokes then responds, inversely if I accelerate slowly there's no choke. Does this relate to the "throttle pedal" since I also have code P0221?

Unfortunately, I am still experiencing the false starts as well, see new videso below.

Video Notes:
- Car will attempt to start but die, with the BAS/ESP light come ON.
- Car will only start properly when holding accelerator while starting, and must keeping revs high! otherwise it will stall and switch off, with BAS/ESP light coming on.
- Sometimes, instead of stalling and switching off it will go into this weird idle mode where the revs will fluctuate around 1.2k and there is NO accelerator pedal response at all (seen in video 2)