Can I export full database and import it in a fresh newer CiviCRM version?
Aivars, If the problem you facing is something related to report then i would suggest to fix the report rather wasting time exporting-importing data/structure from 2 different instances. The problem you facing has nothing to do with db structure. The error in report might be


Any installed extension might be conflicting with report code, so you can probably try after disabling/Uninstalling each extension.
Try creating new report from template, sometimes the form values stored in db for saved reports might have values that are missing/renamed in newwer version.


If you still willing to give a try for exporting-importing data/structure then here is a way how you can do it. The doc is pretty old so you will to need to manipulate with the version you trying.  

HTH

Pradeep