Before clicking on the project icon in the finder window I deleted the duplicated one with the ~ symbol, then I started the project.
Why do you have a duplicated .logic file with the ~ symbol? Why do you delete it?
The reason the exs files are being saved again is because you have ticked the option to save it in the Save assests (Save window). These will then be saved to your project folder.
You don't need to do this unless you wish to transfer your project to another mac with the same exs sample libraries. But, in any case it can be good practice to do this - though does take up more space on your HD.
I can only guess at this point that perhaps the project is corrupted?
try to open the project and select save as...
now choose a new location on your external disk.
make a change and try saving normally. If it doesn't work, try opening some of the Project File Backups in the original project folder.
I've come across the Result code = -48 issue once or twice in 7 years with Logic, so it's not common (for me) and has usually been solved by repairing permissions....
Hope this helps,