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Mass airflow sensors and oxygen sensors are not the same component. A failed mass airflow sensor can definitely cause a check engine light, and they are not an uncommon problem on most cars.
That depends on how many miles you have on your car and what was done the last time it was serviced. Check out RepairPal's info on tune-ups, and then consult your owner's manual. http://repairpal.com/tune-up-what-is-it
Have you noticed puddles forming under your car after it's been parked for awhile? RepairPal has some tips for when you notice a leak: http://repairpal.com/car-fluid-leaks-what-to-do If it isn't leaking out of your engine or cooling system somewhere, then it may be being consumed . . . which is a big problem. You'll probably need the help of a good technician.
This is a tough one. Check out the different stages of the Check Engine Light here: http://repairpal.com/check-engine-light The best thing to do is to find a shop that really knows BMWs--that should help take out the guesswork. The oxygen sensors is a good bet, as those definitely go bad in BMWs as they age. You could take it back to that technician, as they obviously didn't fix the problem for you. If the light is still coming on and going off, there's something else wrong, and I'm worried that if it's left unchecked, you could ruin those new oxygen sensors.
A good way to figure out what your car has is to go to a parts site, like Parts.com, and look up your car and the parts you are interested in. That should help you figure out what your car has. You can also check the services available for your car on RepairPal.
RepairPal offers estimates on newer BMWs for any owner who is outside of their warranty because of really high mileage. Also, some of the information is there to be ahead of those cars coming off of warranty. The prices should be correct! You're right to mention that BMW is the only brand of car that offers a new car warranty for maintenance--including all oil changes, filter changes, and even brakes.
This is not normal at all. It sounds like you've now got a problem, or problems, in your emissions control system. Is your friend a professional technician? It sounds like you now need to take the car to a shop.
This could be for a variety of reasons, as the emission control system is very complex. Take a look at RepairPal's article on the Check Engine Light and emissions control: http://repairpal.com/check-engine-light You will most likely need a professional diagnosis.
Did you change the oil and filter yourself? I believe that the process is fairly complex and may even require a tool. If you had this service done at a shop/dealership, take it back to them and give them a hard time for not finishing the job!!
I'm not 100% sure about your car, but generally when a good technician does a timing belt, they do change any tensioners and even the water pump. The reason they do this is that the amount of labor to change a water pump is the same as the timing belt, and it's really high--and therefore expensive. The water pump part is actually not that expensive, relative to the labor, so it is cheap insurance against the possibility of the old water pump failing and having to do that labor all over again.