linux: How can I view all UUIDs for all available disks on my system?

There's a tool called blkid (use it as root or with sudo),

# blkid /dev/sda1
/dev/sda1: LABEL="/" UUID="ee7cf0a0-1922-401b-a1ae-6ec9261484c0" SEC_TYPE="ext2" TYPE="ext3"

you can check this link for more info

In /dev/disk/by-uuid there are symlinks mapping each drive's UUID to its entry in /dev (e.g. /dev/sda1)

The best command to use is lsblk -f. It will list all the devices and partitions, how they are mounted (if at all) and the tree structure of the devices in the case of using LVM, crypto_LUKS, or multiple volume groups on the same drive.