I don't think the silmarils were the kind of stones that could be split, so a sil sliver doesn't seem possible. Adamant does usually mean diamond, though it could mean any very hard substance, so it's not definite.
My opinion is that the stones' colours are symbolic for their meanings: red for fire, white for water, blue for air. Foster's Guide does say that the blue stone was a sapphire, though I haven't yet looked up any quotes for Tolkien's final word on it.
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'Mercy!' cried Gandalf. 'If the giving of information is to be the cure of your inquisitiveness, I shall spend all the rest of my days in answering you. What more do you want to know?' 'The whole history of Middle-earth.. .'
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