How was the Philosopher's Stone destroyed? Was it ever stated in the first book how the Stone was destroyed? Was the Stone destroyed when Harry dropped it?
There is no in-universe answer. In addition, the Stone was not destroyed when Harry dropped it.
In the first book of the Harry Potter series, Dumbledore tells Harry that he will destroy the Stone. This prompts a discussion about how Nicolas Flamel will die as a result. But in the conversation, Dumbledore never tells Harry how it will be done. The narrator never explains either. Unfortunately, there's no answer to your question.
‘Not the Stone, boy, you — the effort involved nearly killed you. For one terrible moment there, I was afraid it had. As for the Stone, it has been destroyed.’
‘Destroyed?’ said Harry blankly. ‘But your friend — Nicolas Flamel —’
‘Oh, you know about Nicolas?’ said Dumbledore, sounding quite delighted. ‘You did do the thing properly, didn't you? Well, Nicolas and I have had a little chat and agreed it's all for the best.’
‘But that means he and his wife will die, won't they?’
‘They have enough Elixir stored to set their affairs in order and then, yes, they will die.’