Disk cleaning

I can't say much about the first part. I assume they're old coredumps, likely from program crashes. I remember seeing them when KDE Plasma crashed several times related to thumbnail displays.

I use the utility program stacer to clean out unnecessary files. I think it handles the tmp directory too. Haven't had any problems with it. You can also try bleachbit, but I would be careful with that.

Core dumps are memory dumps that some programs might drop after a segfault for debugging, you can figure out which program is printing those using the file command-line utility.
You can delete them, they're garbage unless you want to use them to debug and fix those segfaults or you're willing to report these crashes to devs.

The /tmp directory should be mounted as a ramdisk, if it's not then consider that a filesystem misconfig and address the issue, usually there's nothing important long-term stored on /tmp but some programs might fail, exit or crash if you remove data from them when the system is running, if you mount /tmp as a ramdisk (as you should) everything gets wiped once the system shuts down or reboots.

Great. Thanks to all!