That's a lot of mileage with the original plugs.

In turbo applications it's good to set the sparkplugs around .30 thousandths and some really do suggest to go .25 thousandths(race applications). I know that my ngk plugs show up at the house pre gapped around 40 thousandths.
I would buy one new coil and make sure not to use die electric grease on any of the coils or spark plugs as it will cause mis fire due to the fact that the high energy system for the coils is energy allocated to the coils and spark plugs. And die electric grease does prevent the water and moister from contaminating a spark. BUT! it requires a higher average of electricity to cross a die electric grease path. Like for a car with one coil on a 80's or 90's type distributor application car.
One coil pack(there like double A batteries to me and my mini, just replacing one can keep things going) can stand a chance of resuscitating the coil pack system. As it is new and efficient better at grounding.
Swap that new coil for each(maybe even buy two new coils(I would buy a whole new set if I could afford it.)).
But sometimes one new coils in a bunch don't always work. I find it a better practice to buy about 2 at a time. swap them out one the different cylinders starting the car over and over. observing with the scanner tool. something like
I'll get to my opinion on the battery here in a second but would like to say congratulations on getting your mini to the mileage it has. When I bought my mini cooper back in 2010 it was under warranty sense it had very low mileage and under a extended warranty. If you have a warranty I would take it to the dealership.
Under the practice of a warranty there were things I could have done over the years but some how prided myself off of not wanting to mess with it because of the warranty.
I used to look at the modern marvel under the bonnet of my mini and slightly get overwhelmed it's a good car I dare not mess that up.
I guess what I am trying to say only from personal experience don't get intimated off the big plastic valve cover if it is leaking the gaskets need to be changed or I would at least clean and have o ring silicon grease put on the gasket.
O-Ring Silicone Grease | Super Lube
lightly grease the valve cover gasket for a hermetic seal. Reason why I keep pushing that. Is over the years it was tiny stuff like that. that stage two or to be continued part of changing oil and air filter. for this car. It really depends on no air leaks. Once I figured that out my mini has ran so much better.
You car is throwing all kinds of code possibly due to multiple issues. It's an adaptive program. meaning that actually tries to find a way around things if some module is not performing tip top. but when another module of the power train goes out then the first low performing type thing goes also. It's really what allows the car to safely limp home in most circumstances.
I don't think the ECU is bad at this point. I would think about that as the back wall, Transmission light coming on as the another wall. taking small steps to solve the problem within those guidelines first. If there is electricity and light when you turn the key the ECU YES can still be bad but an optimistic opinion toward that will help. Small engine car and it is not gonna do some super duber full sized car problem or cost as such. In the mechanics,solving the problem as one person, or in it's geometry. It's a small car.
Sounds like you have the IBS battery system in the car that code will need to be erased and reset by a professional or someone with the correct code and scanning software.
if you end up changing the battery.
A fuel filter at 50,000 miles is completely coated in dirt in a mini cooper whether it is the N14 or the N18. An item not a whole lot of people are gonna change if the fuel level sensor is not freaking out. plus it's easier in some sense to just replace the High pressure fuel pump. More than likely no one has changed that fuel filter in your mini cooper unless you did. And that could clear that up!
You should have some sort of variation of this tutorial as yours is not a Diesel. Just get a rough I idea where the fuel tank is under your car. then go into the back of the car. You might need this tool.
Fuel Filter Kit & Lock Ring Tool
combustion chambers all failed........?
that can be resolved but again it would probably cost a bit of money and one of these.
I like this. Do you think I should buy it?
www.lightinthebox.com
A bore a scope unit. although you can probably get them cheaper if you have a i phone or android. as it will be a attachment and an online app of some sort.
Removing the intake manifold by removing the airbox on top of it and the turbo hose clamp right at the intake manifold. It's easier than it sounds. Just to be careful when removing or setting aside all pvc fuel breather hoses. and careful to remove the intake manifold only after the lower pvc breather pipe that is underneath the manifold is detached from it.
Once that is off lower the scope into the intake ports in the engine and inspect the valve stems that about all your gonna see. If they are coated in soot that means you need a wal nut blasting. and would possibly be the cause for all that. But That really would hinge on the idea that your problem has been building for some time with weird stuff going on vs. "it suddenly happened". If it suddenly happened and your valves look evenly coated nothing too bad. Then I would not race off to have that done. Just a inspection you can do. For a 25 dollar- 125 dollar U.S. bore a scope camera tool. Vs being somehow subjected to a 700 dollar wal nut blasting. Of course if it is that latter than you will be out more because of the camera tool.
Point is there are people on this form that can see that cylinder head clean and redone for 700 dollars. Hence is why were all hear to see if there are other methods and better, cheaper ways to solve some of these problems.