Transitive dependency in 3NF
An accepted definition of Third Normal Form is that any non-trivial dependency with a single attribute on the right part must have a superkey as left part, or the right part must be constituted by a prime attribute.

In other words, if you have a dependency with a prime attribute on the right part, that dependency does not violates the 3NF.

For your second question, a relation is in BCNF if any non-trivial dependency has a superkey as left part. If a relation does not have partial dependencies, and all the attributes are prime, this means that no dependency exists with attributes that are not a full key or that are not constituted by non-prime attributes. So, the answer is yes, that relation is in BCNF.