It's the first time I'm printing in CMYK. I can't understand a basic thing. For example if I want to print a shape filled only with cyan color, can I fill it with CMYK(100,0,0,0) (only one ink used) or I must use for example CMYK(100,10,10,10) (every ink is used)?
You can print 100C0M0Y0K if that's what you want.
You aren't required to use all 4 inks all the time.
When you do use all 4 inks, you want to keep the total ink percentage below 300% (known as the Ink Limit). i.e 50C50M30Y60K = 190% total. At no time is 100C100M100Y100K acceptable for anything other than printer's marks.
Talk to the print provider. Each provider may have a different ink limit. Some are 290%, some 300%, some 310%, etc. (320% is generally the maximum though)
Just to complement Scott's answer, if you really are not going to use the other 3 colors, tell the printer so he does not consider this project as a full-color print but one single ink project.
If you send a CMYK project it is considered a CMYK project regardless you are not using but one ink.
Another option is that you do not use CMYK mode, but grayscale images and assign a Cyan color to that project.
You can even send the project as grayscale and simply tell the printer to use Cyan ink (or any color for that matter)