My daughter is getting the message that her disk is full, but we can't delete files to free up space, but whenever I try to move a file to trash, I receive the error message "The operation can't be completed because the disk is full." Please HELP!

Unfortunately the new APFS file system works differently than older file systems. APFS actually requires free space in order to delete items. There is a chance that rebooting the Mac may not work because there will be no free storage space for macOS to use to boot the OS. Your safest option is hoping that there is an APFS snapshot that can be deleted to help free up some storage space so you can delete other files normally. You can find instructions to delete APFS snapshots here:

https://derflounder.wordpress.com/2018/04/07/reclaiming-drive-space-by-thinning-apple-file-system-snapshot-backups/

You should always keep at least 20GB of free storage available at all times for the normal operation of macOS. In fact macOS alerts users when the free storage space drops below 20GB. As you've found out bad things can happen when there is no free storage space with an APFS file system and with the older HFS+ file system running out of space could cause files to become corrupted & overwritten.

I highly recommend you copy any important files to an external drive now while you can still access those files before attempting to reboot into Safe Mode or Recovery Mode.

Read the full thread: Disk full. Can't move files to trash. - Apple Community

Safe mode sounds like the best method.