All spoilers are unmarked!
Art does have a minimum but the trigger for it is incredibly dangerous or involves dying.
In episode three Art angsts about how he has no right to exist which could imply that he may have died at some point.- This theory is supported by the English text in the credits that say Art has an ability to escape death when wounded, however it won't work if he's instantly murdered.
- And thanks to his minimum, he will survive the events of Episode 7.
Moral is a manifestation of Art's minimum.
Or tranversly, Art is something Moral created. Either way the two are definatly connected, the ending heavily hints at it saying something about a "face piece of art". Moral seems to have views that cater to Art, by wanting to make the world for non-minimum holders better, and wanting to save Nice (or Art depending on the translation.) Nice is a Greater-Scope Villain and The Man Behind the Man
Nice's character description doesn't quite match up with how he acts, he is said to be a cunning genius but acts laid back and allows Murasaki to do most of the work. In episode 3 it is revealed to the viewer that Nice is the top secret number one gradute from the academy, which implies that he's incredibly powerful. It could be possible the sound power he uses is not his actual minimum. Art's brother was the one with the forbidden minimum.
The tubes seem to contain the body parts of an early teen, which is about how old Art's brother was when he died. Almost everybody has names made by Facultas
Check episode 7. There is a file Nice's name section in blank. Compare his name with non-Facultas members and you'll see a big difference. Hajime didn't go to Facultas and thus has a normal name. On the other hand, Murasaki has a normal name but you'll have to consider his role in the manga as an agent who had to hide his origins from Nice. Takihiro's mom will help/save Hamatora and/or other Minium holders from a tight spot
I'm sure after her son's death, she will definitely have a turn around. Especially since they helped their son. Nice will receive a major case of Ironic Name
Even now, he is already showing shades of it with some of his actions (he definitely isn't the nicest protagonist out there). What Moral whispered to Art in episode 7 was his Minium
.He states before that it will provide some "good info for him to know" as he is dying so he may have not been talking (completely) out of insanity. Which is probably why he said "Goodnight" since he knew he would come back... I would not be surprised if he knew it from the start.