Official Explanation
Split #1: the Senate of the Roman Republic is a collective noun. Yes, it had many members, but like all collective nouns, it is singular. It would take a singular verb in the present tense, and it demands a singular pronoun --- "it" and "its". Choices (A) & (C) & (E) make the mistake of using the plural pronouns, "they" and their", so these are wrong. Choice (A) compounds the mistake with the phrase "through them they …", using the same pronoun with two different antecedents.
Split #2: The word "decrees" is plural and demands the plural pronoun. (C) & (E) make the additional mistake of referring to "decrees" with the singular pronouns.
Split #3: the comparison. We are comparing the subject to subject, noun to noun, so the word "like" is perfectly acceptable ---- "decrees …. like laws". This is what (A) & (D) have. If we use the word "as", we need a whole phrase --- the construction "as was the law" in (E) is acceptable but wordy. The "as" + [noun] construction of (C), "as law", is not favored by the GMAT. Choice (B) has the atrocious "as if to be law" --- wordy, tentative, hypothetical, and grammatically incorrect: take that out back and shoot it!
The only possible answer is (D).