The idiom "foot the bill" means to pay the entire cost of something, especially when it is unexpected or someone else's responsibility. It does not mean a literal or symbolic action involving a "bill," and it's used in financial contexts.
I: Correct Usage - Anika is taking on the financial responsibility of paying for a group meal, even though she wasn't the primary consumer. This is a textbook use of the idiom.
II: Correct Usage - Correct usage - Though the situation is questionable ethically, the idiom is used correctly to mean "pay for the cost."
III: Incorrect Usage - The phrase is interpreted literally and symbolically, which misunderstands the idiom. Physically kicking or destroying invoices doesn't equate to actually paying them, so this is incorrect.
Thus, option (a) is the right answer.