Question: Is it possible to manage IT maintenance operations like a project, with typical project management mechanisms including scope, time, and cost planning? In our project we experience difficulties in such a management of our IT infrastructure support department. We don't know how to define their scope, how to control it, and how to make sure that the work is done. They are not developing any software but organizing our server space. Sometimes (and very often) their mistakes severely affect the entire project. I'm interested in finding some formal or semi-formal instruments on IT department management and coordination with the rest of the business.

Answer: 
[ITIL](http://en.wikipedia.org/wiki/Information_Technology_Infrastructure_Library) may help you.
When I have had support responsibilities I found it was a very successful week if I got the planned work done on two days. A lot of support time may be taken up responding to problem reports. Even if the problem is out of your control you still need to determine that it isn't in your control. You may then need to manage the response to the problem. 

There are projects (usually on the small side) within the work that the support group will be handling. Setting up a process to make those happen could be worthwhile.

The one area ITIL is reported to be best suited to is managing support groups. I would consider implementing that area of ITIL.