Unfairly criticized during his time, Emperor Claudius expanded the Roman…

Answer: and passed laws that protected the rights and freedoms of Jews throughout the Empire.

Explanation — Parallelism:

The sentence lists actions in the same tense: expanded, constructed, and ... Therefore the third verb phrase must also use the simple past tense to be parallel. "And passed laws that protected" uses the simple past verb "passed" and a relative clause describing the laws, so it matches the other verbs and is correct.

Why the other choices are wrong or inferior:

• The phrase "having passed laws for protecting" uses the participial "having passed," which breaks parallelism with the simple past verbs. In addition, "for protecting" is awkward and not the idiomatic way to express the purpose of the laws.

• The phrase "having passed laws to protect" also begins with the participial "having passed," so it fails the required parallelism. Note: if the sentence used "and passed laws to protect," the infinitive "to protect" would idiomatically express purpose and would be acceptable, but the given form is not parallel.

• The phrase "having passed laws that protected" contains a correct relative clause "that protected," but starts with the participial "having passed," making it non-parallel with the other simple past verbs.

Conclusion:

Because the sentence requires parallel simple past verbs and the relative clause "that protected" correctly describes the laws, the correct phrasing is the simple past construction beginning with "and passed", followed by "that protected...".