You have put the wrong oil in, but that is not such a problem
The biggest problem is you let the oil light come on, not sure about the very latest models, but none i am aware of have an oil level sensor, so when it gets low enough to set off the oil pressure light, you are way too low.
At this point putting almost any oil you could get your hands on in was the right thing to do
10w40 is not necessarily any different to 0w40 or 5w40 at operating temperature but at cold temps when you start up it is a lot thicker, especially at sub zero temps, with a good fully synthetic 10w40 oil you would probably not increase engine wear significantly unless you were starting up in -15 or below ambient temps, but if you are not running the correct oil long term you can run into problems regardless of the SAE grade being correct for the climate or not, the ACEA grade is just as or maybe even more important when choosing oil that is not bmw longlife approved. but a week with the wrong oil is not going to significantly increase the wear on your engine, infact even the cheapest mineral oil that's new will probably give better protection at this point that the oil which has done a year or 2 in your engine, if any damage shows up it'll be the result of you running it low not putting in the wrong oil for a week
1L may still not be enough depending on how low it was, if it's still under warranty you will want to make sure it's above the min line on your dipstick before putting it in for service, and not mention that you put in the wrong oil, there is no real way for them to find out unless you tell them.