To move the installation (including database), you can simply move the entire cryosparc folder. Just make sure that you edit your ~/.bashrc file to change the path there that points to cryosparc/bin.
To move the output directory, you can use the CLI tool:
cryosparc configure bulk add <path/to/new/output/location> <short_name_for_output_location>
cryosparc configure bulk primary <short_name_for_output_location>
These commands will instruct cryosparc to use the new path you want as it’s new output directory. Results that have already been stored in the old output directory will not be moved. If you need to move old outputs let me know, this is a bit more advances.
To change the SSD cache location, inside the cryosparc installation folder, locate the directory called run. Inside this directory you will see a directory (actually a symlink) called cache. You need to first delete all the files inside the cache folder, then delete the cache symlink itself, then create a new symlink to the new cache location you want:
ln -s /path/to/new/cache/dir ./cache