Question: End of Nov 2018 I took the Mini for tire rotation and told the garage I was taking a road trip and to check all fluid levels including the oil. When I picked it up they confirmed this was done. The oil change was due for the end of Dec. Jan 3 I check the oil level and the dipstick was showing very low oil level (540 miles driven). I opened the reservoir and it was empty! There were no visual oil leaks. Is it possible for the oil level to go down so much if they had really checked the oil levels at the shop?  

On Jan 3 the performed and engine oil system flush and synthetic oil change.

In April the car started to run rough and cold start issue. Engine light came on and towed to garage. They said cylinders 1,3,4 were misfiring. Replaced all the coils and spark plugs. They also performed a throttle body/fuel injection service. 

Early May the car still having cold start issues. Towed back to the shop. This time all injectors were replaced and valve cleaning.

Picked up the car on a Friday and by Tuesday the car was having the same cold start issues. This time they want to replace the high pressure fuel pump and purge valve.

Are all these issues related to the low oil levels? What damage was caused to the engine? Is there something else going on with the engine? It's become a money pit!

Answer: 
This could be either a drive problem, or an engine problem.

One easy check for whether it's a transmission problem is to put it in neutral, and see if the problem continues. If it does (stays relatively the same), then it's not a transmission problem (your transmission is disengaged). If it's a transmission problem, you'd start by checking fluid, and then trying to narrow it down to the transmission or the differential (probably one of those two).

I'm leaning toward it being a drivetrain problem, since that seems to match the symptoms, although the codes don't quite match. Since it doesn't change with how fast the car is moving, that limits it to the transmission.

If it's not a transmission problem, then it's an engine problem. The engine needs three things to run: fuel, air, and spark. So you'll have to start by narrowing it down to one of Gas, Airflow, or Electrical. 

* If you smell gas while the problem is happening, that probably means that the problem has to do with gas not being burnt when it should. So it's getting gas, but not burning it. Electrical or Airflow.
* If it's a gas problem, it will probably be related to how much gas you're giving it. You mentioned that it doesn't have to do with whether you're accelerating, so my guess is that it's not a gas problem.
* Electrical: Your engine codes seem to suggest that it might be an electrical issue of some sort. The first code might've just come on because the engine was running really rough, and the second one would tell me that the car isn't burning all the gas it's getting. You'd want to check spark first, then move to the more complicated parts such as your O2 sensor(s), MAF/MAP sensor, knock sensor, etc.
* Airflow: If it were airflow, restarting the car wouldn't help.
Supreme gas is overkill. I would consider another cleaner like Seafoam who makes a fuel additive and top cleaner sprayed into the intake. Search youtube for info on that. They even make crankcase cleaners. 

In an 07, when was the last time you changed the transmission fluid? If there is a large fleck of metal floating around your transmission that would wreak havoc if the fluid hasn’t ever been changed. 
If you have a dipstick, Red is okay, black fluid means change immediately.
Otherwise make sure the engine oil is changed sooner than every 5000 miles.