Trouble in cold weather

Sounds like the cold start solenoid. It is designed to keep the engine running at a set RPM until it reaches a specific engine temp.

It sounds like a faulty idle air control valve. The computer uses the valve to control idle speed by regulating the amount of air entering the throttle body. Its possible the motor inside the valve is weak, or the valve is gummed up. I would unplug the valve when base idle is near normal and drive it for a day or two. If the valve is the problem the idle speed should stay in one place. And it should set a trouble code for the valve being disconnected.

No way to tell what happened with the high idle if you can't make it happen on demand.
The oil and engine lights would come on if the engine died while the key was still on so that was a normal event.
You might stop somewhere and have the computer scanned for trouble codes just in case the computer recorded anything.
The difference in octane should not be a big problem if you don't switch back and forth, after about 50 miles of driving the computer will adjust for the octane of the fuel.

READ THIS (happy ending so far...):
audi a4 2L turbo quattro, manual transmission with 98,000 KM. Perfect conditions, no oil leaks whatsoever.

Left the car off for two weeks in very cold weather (-10C down to -25C). When I restarted, it started immediately but with heavy rattling noise due to camshaft adjuster not getting enough oil pressure. After 3 minutes of warming up (outside temp.: -12C) at very low rpm (below 2,000rpm), I start moving the car. Still hearing heavy rattle noise. As soon as I pass 2,000 rpm, I get a scary red warning, low oil pressure. Turn off the engine immediately. In 1 minute, I re-start the car and the engine lights check ok, so I drive in first gear super slow (1,200rpm) hearing the same rattling noise. After another minute, finally the noise all the sudden disappears and the car starts running just fine.

Called Audi dealer and they told me that in extreme weather conditions, I should warm the engine for 10-15 minutes if necessary before start moving.
Take away: luckily, I didn't screw up the engine since I was using it at extremely low rpm (easy to do with clutch and manual transmission) until the oil reached full pressure. I am pretty sure now that the problem was leaving the car off for such a long time in freezing weather. All the oil flows back to the bottom, and when I restarted it, the cold oil with high viscosity took a long time to reach all the parts of the engine, specially the camshaft adjusters that are actuated by using oil pressure. Next day, the car started at -9C perfectly without making any noise (as usual). Basically, the longer you leave your audi in cold weather, the longer you might hear the rattling noise until the oil reach full pressure inside the engine. My car took 6 minutes to fix it after couple of weeks in cold weather. This makes sense to me; in fact, in the past I only heard the rattling noise after leaving the car off for a couple of days in the winter.
So far, this has had an happy ending....

http://autorepair.about.com/cs/generalinfo/l/bl703.htm

It sounds like a MAF sensor is dirty or faulty, clean first with gumout then replace if problem persists.

try coolant temperature sensor

Change your Minis Mass Air Sensor this will solve your problem.

probably is a emissions sensor problem, lots of these parts are plastic. check out the throttle cables, lub em wd40. there is a type of valve somewhere on top of engine, it may be cracked, pcv valve stuck. lots of possibilities, almost too much for solution online. something emmissions with an electronic sensor is acting up.

Here is the most common cause of surges and stalls and low idle, it is the idle speed control air-bypass valve and throttle valve (IAC for short), they get full of gunk over the miles and cause idle issues (stalls, low idle) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake