"Complicated" or "complicating"

Solution 1:

I am assuming it is because "complicating" cannot be used as an adjective - it can only be used as the present progressive form of the verb "complicate."

Exactly right. The word "confusing" has the form of the present-progressive, but it can also be used as an adjective (Source: Oxford Learner's Dictionaries). This is just a fact about the specific word, so looking up in the dictionary like you did is the correct course of action here.

Because "heavy" is an adjective and "complicating" is a present participle, your sentence C) seems a bit odd to me. There's a kind of "zeugma" where you're making "is" serve two roles: as a copular verb and as an auxiliary verb. (These grammatical roles are usually differentiated; see "Is "am" in "I am right" an auxiliary verb?". But, keep in mind that some people refer to "be" as an "auxiliary verb" in all of its uses, whether or not it is "helping" a lexical verb.)

To avoid this, I would add a few more words to change the structure:

(C2) "The topic of landmines is very heavy, and it is complicating the peace talks."

Solution 2:

While there are exceptions, normally when you want to turn a verb into an adjective, you use the past tense. complicated is the past tense of complicate, and can be used to describe something. complicating is the present tense, so is not generally used as an adjective.

In (C), you're not using complicating as an adjective, it's being used as a verb, to refer to what the topic of landmines is doing (it's causing the peace talks to become more complex).