Can I use in Omeka Classic any set of elements, which is not Dublin Core? Or extended Dublin Core? In short, any other fields expect for the default ones?
Plugins in Omeka Classic can add additional element sets (or add to existing ones, as in the case of Dublin Core Extended).
Some of the plugins in the directory do this for various metadata standards: VRA Core is one I can think of off the top of my head. Some other plugins use elements sets for storing data for the plugin’s usage, like the YouTube Import plugin.
You can also create your own elements using Item Types.