You may want to have a look at
which documents most of the above. The easy (and correct) solution for loading .fzpz file is to either double click on them or us File->open then select the .fzpz file in the file system. That will load the part in to the mine parts bin and if you save it when exiting Fritzing it will be there in the mine parts bin when you next start Fritzing. To get a part in to core parts you need to make a pull request against the repository on github. Right clicking on a part in the mine parts bin then selecting export part will export the part as an .fzpz file for archiving (which is a wise idea as it is possible to corrupt the user directories and lose the contents of the mine parts bin.)
Peter