This is a classic case of parallelism, but with some twists. The confusion here usually comes from being unclear about which "verbs" should be verbs, and which should be "-ing" modifiers. (For more on "-ing" words and an explanation of why they're rarely verbs, check out our Topic of the Week:
https://gmatclub.com/forum/experts-topi ... the%20week)
Let's start with the first underlined word: we have a choice between "broadens" and "broadening." "Broadens" is a verb, and it's parallel with "puts on an impressive bluff" in (A) and (B). "Broadening", on the other hand, is a modifier, giving us extra information about what happens when the snake puts on its bluff -- and that makes much, much more sense. So we can get rid of (A) and (B).
(C) strikes me as being unbelievably long and wordy, but so are all five answer choices.

More usefully, the parallelism looks OK: "broadening and feigning" are parallel modifiers, both of which continue to describe the snake's "impressive bluff". The pronoun "it" is fine, too: because it's the subject of a new, dependent clause ("but it has no fangs..."), the subject unambiguously refers back to the subject of the first clause ("the hognose snake"). (If you want to read more about this type of pronoun issue, check out my post in this thread:
https://gmatclub.com/forum/china-s-vast ... l#p1838737. We'll also address this in an upcoming Topic of the Week.)
(D) is easier to eliminate: the modifier "broadening" and the verb "feigns" are clearly not parallel.
(E) replaces the "and" before "feigning" with a comma, and that doesn't seem ideal: the sentence is clearer if the two modifiers are in a parallel structure, but I'm not sure that it's a huge problem. The bigger issue is that we don't have a new clause at the end of the underlined portion, because the "it" has been replaced by "with." That causes a problem down the line: at the end of the sentence, we don't have a subject for the verb phrase "will fall over and play dead." So (E) is gone, too. )
We're left with (C). In real life, I think it's a wordy, crappy sentence. But that doesn't matter! It's free from egregious errors, so it's the correct answer in GMAT-land.
Do options A and B repeat the error in E ? (not having a subject for the clause after