Mac mini won't start in any mode. Looks to be some kind of disk failure
Right after the root# prompt, enter the following:

/sbin/fsck -fy


Press the Return key.

Background: You can repair a drive by using the fsck command. Fsck stands for File System Check (the name is sometimes referred to as File System Consistency ChecK); it can be used with various optional parameters.

It will take a few minutes. 

In the end, if your drive was OK, the screen will say “The volume (name of your hard drive) appears to be OK”. If any repair was made, you’ll see the prompt, “FILE SYSTEM WAS MODIFIED”. Then, you’ll see the root# prompt again.

Right after the root# prompt, enter the following:

reboot


Press the Return key. Your Mac should restart normally. Let me know how it goes.