Misplaced or Dangling Modifiers

REVIEW: Is the sentence correct or does it contain a misplaced modifier?

The car needs to go to the shop that is out of oil.

What are dangling modifiers missing?

Which part is the dangling modifier in the sentence below?

Running around, an ankle was broken.

Is the sentence below correct or does it contain a dangling modifier?

After answering the question, Kasey earned a piece of candy.

Is the sentence below correct or incorrect?

Listening to music while walking home, an accident was not noticed.

Which sentence best corrects the dangling modifier?

Listening to music while walking home, an accident was not noticed.