Learn Russian: Неужели ты нечаянно сломал ей каблук? - Did you really accidentally break her heel?

This is the dative of detriment. In Russian, when you do something to a person's body part or clothing—especially if it causes harm or disadvantage—you put the affected person in the dative case (ей) and the object in the accusative (каблук). Saying сломал её каблук is grammatically possible but sounds much less natural, as it loses the feeling that she was personally affected by the mishap.

Does неужели just mean 'really'? How is it different from asking with разве?

Both words ask for confirmation, but неужели expresses strong disbelief, shock, or surprise. Разве is typically milder, often just expressing doubt or seeking reassurance. Here, the speaker is genuinely shocked about the broken heel.

Could I use случайно instead of нечаянно for 'accidentally'?

Yes, they are often interchangeable, but нечаянно specifically emphasizes that an action was unintentional or a clumsy mistake (like breaking a heel, dropping a glass, or bumping into someone). Случайно is broader and often translates to 'by coincidence' or 'by chance' (like randomly running into a friend on the street).

What case is каблук in, and why didn't it change its ending?