Check -
http://arduino.cc/forum/index.php?action=stats - for interesting facts and figures.
1. How much Arduinos were sold per year / month ?
This board has had ~65000 unique registered members.
The site has often 4x as much guests as members logged in.
So there are 250.000 Arduino users in the world. (yes, you have lies, damned lies and statistics

Lets assume they use on average 2.5 Arduino's per year, some will have only 1, others use 10 per year.
That gives 600.000 Arduino's per year, ==> 50.000 per month.
2. How do they get the project known ? (advertising)
Yes.
3. Do they get faster into the market because of open source ?
Dont know, not all people are charmed by open source, but many are. Germany is a country with a very high OS factor, while the other countries this is less.
You could do a search on linux demographics, think that has been investigated. That would give some sort of measuring stick/indication how many people like OS.
4. The Arduino group produces the Arduino, do they give a guaranty ?
Don't know.
But they guarantee that they do their uttermost best as they all have Arduino as middle name. If they produce bad stuff all the users of Arduino will point to them.
Please be aware that most anonymous engineers at most big companies can produce crap without the world knowing their name.
5. The Arduino project started as a „closed“ project (you developed the first boards of your own) later it was made „open“ (the community was invented to improve the board), why didn't they started it open ?
Don't know if it was ever closed, but still that is just a business model decission, I think it is a sign of the time, read the book open innovation of Chesbrough. Many projects have gone open and created a crowd around them. Many failed and some succeeded, and tomorrow the world will be different agian

Please post your final report on this forum,
(All above is just my honest opinion / best guess, not an academic source)