The hognose snake puts on an impressive bluff, hissing and rearing back,
broadens the flesh behind its head the way a cobra does, feigning repeated strikes, but, having no dangerous fangs and no venom, eventually, if its pursuer is not cowed by the performance, will fall over and play dead.
Option Elimination -
Basics first - Comma + ING is adverbial. Here, we are trying to explain the "How" part of an action "puts an impressive bluff."
So the basic structure here is Clause, modifiers, but clause, and clause.
(A) broadens the flesh behind its head the way a cobra does, feigning repeated strikes, but, having no dangerous fangs and no venom, - "broadens" is a verb and can be parallel to "puts" but that doesn't make sense. And also modifier parallelism is also broken; we have a clause, ING modifier, verb, and ING modifier. Moreover, after but and before "and," we need a clause for parallelism. But we have a modifier after but.
(B) broadens the flesh behind its head the way a cobra does and feigns repeated strikes, but with no dangerous fangs and no venom, - again, this has verbs "broadens" and feigns" instead of the ING verbal to explain "How." Moreover, after but we have a modifier and after "and" we have a clause. Not good.
(C) broadening the flesh behind its head the way a cobra does and feigning repeated strikes, but it has no dangerous fangs and no venom, and - Perfect. It refers to "the hognose snake."
(D) broadening the flesh behind its head the way a cobra does and feigns repeated strikes, but with no dangerous fangs and no venom, and - same issues as explained earlier.
(E) broadening the flesh behind its head the way a cobra does, feigning repeated strikes, but with no dangerous fangs and no venom, and - same issues "but" and "and."