Question

You roll a balanced die two times. Is the second roll independent of the first roll?

Answer 1

Yes it is. The die has no memory.

So the outcome of the first roll does not influence the second, or later rolls.

This only works if a die is perfectly balanced - which it never is, and that's why dice are changed every now and again.
And the surface on which it is rolled must not interact with the die (like being slightly wet or sticky or static).