I think you can delete the PI_temp and PI_install files without issue. PixInsight creates many temp files to help speed up processing and the PI_install is most likely where the PixInsight application was downloaded before the installation. After deleting the PI_temp folder, I would restart the computer.
Actually, you always should remove the directory where you have uncompressed the installation tarball file. If you uncompress a new version on the same directory where you uncompressed a previous one, there is a risk of mixing files from two versions, which may cause problems.
Admittedly, this should be improved. A future version of the UNIX/Linux installer will prevent these potential issues.