For starters the parts editor was incomplete when development stopped in 2016 (I believe work is going on to improve parts editor now development has restarted though but it hasn’t been released yet.) That said, with the warning that I don’t use parts editor often, AFAIK parts editor doesn’t actually edit parts (at least at the level you want to.) You need to export your new part as an .fzpz file by right clicking on the part in the mine parts bin then select Export part. That will write the part to a .fzpz file in the file system. Then you need to unzip that .fzpz file, which will give you a .fzp file and 4 .svg files. In this case you need to edit the pcb svg file with an svg editor such as Inkscape and move the pins a bit closer to each other, then save the svg fille (leaving the groups as they are configured as they are required!) and preferably run it through FritzingCheckPart.py (available here)
to remove the px in font-size (among other changes) or edit the svg with a text editor and replace all the font-size=“35px” with font-size=“35” because Fritzing objects to the px on the font size (and Inkscape adds them for CSS compliance!) Then you can (as I do) rezip the .fzp and the 4 svg files in to a .fzpz file and run that through FritizngCheckPart.py to clean it up, then load the .fzpz file in to Fritzing as your new part either by File>Load>your_fzpz.fzpz or double clicking on the .fzpz file. Or you can edit either the original part or your new part with parts editor and in pcb view click “File->Load image for view” and point it at your new svg file. That loads your new svg in to the part (effectively replacing the pcb svg file with your new one) and then save that as a new part. I find modifying the files to be easier than dealing with parts editor. These 2 tutorials apply to the current versions of Fritzing. The video tutorials cover parts editor, but mine does not (other than to tell you why I don’t find it useful!)
Most of the others are for versions before parts editor was created. If you have problems feel free to post the .fzpz file or .fzz file (the entire sketch) and one of us will look it over and tell you what is wrong.
Peter