1. (A)(B)…new evidence undermining the theory…
(C)(D)…new evidence to undermine the theory…
(E) …new evidence that undermines the theory…
In all cases, the noun new evidence is modified by the following phrase. Arguably, “to undermine” implies intent in a way that “undermining” and “that undermines” don’t, but maybe that’s the intended meaning. I would keep all of these as possibilities.
2. (A)(D)(E) … theory of a plague …
(B)(C) … theory that a plague …
“of” seems unidiomatic to me. You might have a theory about something, or a theory that something is true, but only the “theory of relativity” or the “theory of evolution” come to mind as good theory of something examples. The indefinite article in “a plague” makes it much less iconic than relativity or evolution as something you might have a “theory of.” Even as a native speaker of English, I wouldn’t rule out ADE based on this one, though.
3. (A)(D) …theory of a plague caused by (something) that contributed to the deaths…
(B) …theory that a plague caused by (something) contributed to the deaths…
(C) …theory that a plague was caused by (something) and that contributed…
(E) …theory of a plague that was caused by (something) and that
NOTE: In all choices, (something) = a rapid increase in pest populations
#3 is really several splits, but I think you have to consider them together. Both “of” and “that” following nouns indicate modifying phrases. In the choices that have “and,” we need to look for parallelism. Finally, “caused by” after plague is a modifier (i.e. it answers the question “which plague?”) whereas “was caused” after plague is a verb. What do you all think about these issues?