I am not sure I understand what you are asking with regards to numbers 1 and 3. It isn't necessary to 'save' anything. Edits made to photos are saved automatically as they are made.
With regard to item 2, the filename is contained in the Info panel (located in the bottom right of the interface). It is necessary to either click the icon or use the keyboard short cut key [ I ] to expose the panel to read the filename.