Help! Misfire cylinder 4, carbon deposit on spark plug cylinder 3

[albatross_nlv]

Hello everybody,

I’ve been browsing this awesome forums in the background whilst enjoying my 1series, but now I am in trouble myself so I guess it’s time for me to step within this community. This is my first post within any forums ever.
I’ve been reading everything I can find on the forums, but couldn’t get to a point where I am sure what the root cause is and the most recent discovery makes me doubt everything. I am technically gifted, but I am not working with engines every day. I believe I know what I’m doing but if I run into something that doesn’t make sense then it’s back to the planning board.

I’m driving BMW E88 118i N43

Lets get on to the problem:
Driving whilst on low revs (I remember driving for a while and only on/close to idle I got it. I got a misfire on cyl4 P0304. Another code said the burning duration was too short: P1304. Together with that came NOx sensor codes P124D, P122C, P121F P122F, P127A. Lambda codes P114B, P2196.
My first suspicion was carbon buildup on the intake valves. I had already replaced the coils on 3 & 4 (third was still using old Delphi coil that was completely rusted and the fourth cylinder had a misfire back then when I thought I fixed it.)

After looking at this I am quite confident it cannot be the carbon buildup. I am going to clean the valves during the weekend anyway, but now I’m looking past that.
However I decided to inspect inside of the cylinder to see if I can find a pattern and upon removing all of the spark plugs I noticed there’s a lot of carbon on the spark plug from cylinder 3.

Here’s the video of cylinders, I spot chipping on 3rd and 4th cylinder but I have very basic expertise so I’m not really sure what I should see or not.

I have ordered one refurbished piezzo injector and plan to replace the fourth injector, but as I see the carbon on the spark plug of cylinder 3 I’m not sure if I shouldn’t replace the 3rd one as well.

I hope that I have provided enough info and that whoever takes the time to read it will have a great day. I’m personally running into a knowledge wall where I’m seeking someone who knows what I’m trying to describe.

If I had to guess I'd say injector 4 has a bad spray pattern/doesn't spray enough and injector 3 is leaking, but I don't know how to test this nor have any experience with this.

Also could someone advise me with a good book on direct injection?

[albatross_nlv]

I received the wrong revision (3rd) injector that I cannot combine with my current ones (11th), browsed around here to find that there's mixed feelings about the compatibility, so I decided to give it a try.
The issue became hardly noticeable, when calibrating the fuel system (doing the initial drive) I could not get the last set point to become active. The car drives OK, especially when warm, but now when cold it still has misfires for the first few seconds or until I rev the car.
Next step is to install 11th revision injector and I'm going to do that anytime soon, will keep this thread updated.