Question

Mutations in dna sites such as promoters and operators can act only in cis

Answer 1

This is true.
An easy way to remember this is that Cis-acting elements are physically linked to a set of structural genes. So promoters and operators are physically linked to the gene they express. They are cis acting because they are on the same strand as the structural gene they control.

On the other side, trans means that they can come from somewhere else and act. A good example of this would be regulatory proteins. These could be expressed somewhere else (or on a different strand) and then bind and affect transcription.