System preferences are stored in various files under / and user preferences in dot files under /home/<user>/. There may be a problem saving the files to the Live USB because of the way the permissions are organised but, in any case, if you copy them to another USB, they will not be available when you next boot. So you would still have to re-enter them.
Rather than running the Live version, you could in theory install Leap to a 64GB USB and configure the BIOS to boot from it. What are you trying to achieve?
I advise against saving preferences that make the system freeze
Typically, on a live USB, a “hybrid” partition is created and used as an overlay (“overlayfs” I think). So preferences and other changes are saved in that overlay. This mostly works, though you cannot update kernel or boot parameters that way (those are used before the overlay partition is mounted).