Basis of a Boolean Algebra

Question

I have a construct that I proved forms a (finite) Boolean Algebra of sets over a given universe.

My questions are as follows:

1. Do I immediately know that there exists a unique basis for it?
2. If yes, is there a generic way of constructing it?
3. Given the finiteness property, I know my algebra is atomic. Are these atoms precisely all the elements of my basis?

Thank you!