Corsa high fuel consumption and stalling

Sounds like a classic case of a failing mass air flow (MAF) sensor, or LMM as you called it. The symptoms you are seeing all point to that. Higher fuel consumption happens because the engine computer isn't getting correct data about how much air is entering the engine, so it messes up the air-fuel ratio. Check engine light is another big clue. Out of curiosity, have you tried cleaning the MAF sensor yet? Sometimes that can resolve the issue temporarily.

I haven't tried cleaning it yet. Where is it located, and is there anything special I should use to clean it? Also, if it's the MAF, would that also explain the smoke I'm seeing on acceleration?

The MAF sensor is usually located in the intake ducting, right after the air filter box. You'll need a special MAF sensor cleaner – don't use anything else! As for the smoke, yes, a faulty MAF can definitely cause that. The incorrect air/fuel mixture can lead to incomplete combustion and thus smoke, which I am sure is not a fog but rather a sign that unburned fuel is being expelled. Given the mileage and those combined symptoms, it may be time for a new MAF. For peace of mind and a precise diagnosis, I'd suggest a reputable shop.

Thanks for the insight! Seems like a trip to the shop is indeed in order. Replaced the mass air flow sensor for 365€. Runs like new now.