Lot of questions ;) Please find my answers below
What kind of things will background check check at consultancies in Europe and Middle East?
Just if what you wrote in your CV is true and your criminal record
Do I need to provide contact information for every previous employer?
Usually they have agencies doing the check so no need for you to provide contact information
How many do they ask for?
The ones I saw were for the whole job experience/education
Do I need to provide every address I stay?
Can I not put a short stay at a company (which I left after two months)?
You mean in the CV? Yes, you can avoid to add it
Do I need to put exact date of start and end of previous jobs? (I only remember the month, not the date)
Month only is fine
What else? What are some guidelines and what does it include?
If what you wrote in the CV is true you really don't have to worry about this step. Better to focus on the prep for the interview ;)