Over the years, "dice" has become an acceptable description for a singe die. Almost everyone now speaks of "a dice". Those who insist on calling it a die are regarded as being overly pedantic. "Dices" is never used - "dice" is used for one or more.
However, we still say...."The die is cast" when we say something has been decided and cannot be changed.
2. We usually "throw" dice, but we can "play dice". I think Einstein is said to have said, "God does not play dice with the universe".
We also "roll" dice.
We "dice with death" every time we cross a busy road, so yes, we can use it as a verb. A tightrope walker "dices with danger" and so on.
3. I don't know of any special names for faces other than "snake eyes" when two ones come up together. I'm sure other posters can help here.
4. I'm not a gambler, but I think they sometimes call dice "bones".
Hope that helps
buggles(not a teacher)