Did Tim Anderson’s Bat Flip Cross the Line?

Last night Tim Anderson of the White Sox hit a home run against the Kansas City Royals followed by flipping his bat in the direction of his own dugout. See the video below.

In his next at bat, the Kansas City Royals pitcher hit Anderson with his first pitch squarely in the hip. This led to the following.

Umpire Joe West eventually ejected Royals pitcher Brad Keller.

Questions:

Did Tim Anderson break one of baseball’s unwritten rules with his bat toss?

Was Brad Keller justified in exacting retribution in the form of hitting the batter with a pitch?

Who is most to blame for the ensuing fracas?

Is this type of thing an inevitable result of ”bat flipping” and if so is that sufficient reason to discourage it?