At the annual stockholders meeting, investors heard a presentation on the numerous challenges facing the company,
including among them the threat from a rival’s multibillion-dollar patent infringement suit and the declining sales for the company’s powerful microprocessor chip.
A. including among them the threat from a rival’s multibillion-dollar patent-infringement suit and the declining sales for
B. which includes the threat of a rival’s multibillion-dollar patent-infringement suit and declining sales of
C. included among these the threat from a rival’s multibillion-dollar patent-infringement suit as well as a decline in sales for
D. among them the threat of a rival’s multibillion-dollar patent-infringement suit and the decline in sales of
E. among these the threat from a rival’s multibillion-dollar patent-infringement suit as well as the decline in sales for
A) "including" indicates an adverbial modifier. This could mean that the investors were including the threat, and that wouldn't make sense. We also have two possible antecedents for "them": investors and challenges. If "them" refers to investors, it doesn't make sense. (Normally, I'd ignore this possibility, but the use of "including" suggests that we might be talking about the investors.) If it refers to challenges, then, as Eli said, it is redundant. It would be better just to say "including the threat."
Also, "sales for" is also the wrong idiom. We want "sales of." Right there, we can get it down to B & D.
B) "which" indicates a noun modifier and "includes" is singular, so we are saying that the company includes the threat. Again, that meaning doesn't work.
C) "included" indicates a noun modifier, so it should modify the preceding noun. But what is included? The threat and the decline. We can't use "included" to modify what follows. Also, this choice has "sales for" again.
E) "sales for" again. Also, "as well as" without a comma isn't very good, especially when we have the option to just say "and."
As for "among them" vs. "among these," our choice depends on context. Here, the choices with "including"/"included" have other meaning issues, so it's hard to make a determination. Between D & E, "among these" is the more problematic construction. We can modify a preceding noun by saying "among them the X," but this is an idiom. "Among these" simply doesn't work the same way. If we had two separate sentences, it might work: "At the meeting, investors heard a presentation on the challenges facing the company. Among these were X and Y." Notice that here, the implied meaning is "Among these (challenges) were X and Y." In D & E, we are using the "among" phrase to modify "challenges," so it is redundant to add "these."
I hope this helps. Let me know if I can clarify any of the above.
_________________