That's really Jamie Dornan singing, and it was his choice to tear his shirt off at the end of the song. He wasn't supposed to--on the commentary they mention the shirt wasn't designed as a tear-away--but he felt it was necessary.
They wrote and/or shot scenes for a montage of reasons why Barb and Star had been fired including writing notes with a Sharpie on the furniture, riding a moped through the store, and jumping out of a cabinet to scare a customer who then proceeded to have a heart attack.
Kristen Wiig and Annie Mumolo have been writing comedic, middle-aged ladies since their days back in The Groundlings, the legendary LA improv group.
The opening onscreen definition of "culottes" was added late in editing as they all realized that most folks don't know and love them to the same degree as these three filmmakers.
The end water fight was shot in the actual ocean, not a water tank.