nevermind: I know that in InfoPath there is no possibility of storing data to display later (am I right?)
No, the data can be stored in embedded resource files, default values and choices of data fields/controls if not mention "external" data sources.
nevermind:
Can you advise me if it's possible?
This is possible
It would have been funny to create forms without ability to persist data or do all mentioned by you
nevermind:I know that SharePoint is integrated but I don't know how it can be used (or if it can be used)
This is generally being done by clicking on on Infopath Designer GUI (menus, buttons) and using wizards and choosing choices from drop-down list boxes