In an attempt to attract more tourists, the Swiss government

Dear WoundedTiger & Himanshu,
Let's distinguish between (a) what's possible in the wide world of grammar, and (b) what the GMAT will ask you about. As it turns out, those two are not coextensive --- there are all kinds of subtle grammatical oddities that the GMAT SC will not touch with a ten-foot pole.

First of all, yes, this sentence,
The Swiss Government commissioned statues, having them decorated by local artisans.
by itself is 100% correct, and could be the correct answer to another, hypothetical SC question.

Here's the thing, though --- if the GMAT gives you a sentence of the form [subject] [verb form], [verb form], "and" [verb form] ---- then either
(1) all three verb forms will be the same or in parallel --- that's true over 97% of the time --- that's a very good default assumption to have
(2) in a rare case in which, say, the second verb form is an entirely different kind of activity, such that it would be [u]unambiguously impossible for the subject of the other verbs to be the performer of that particular activity[/u], then, yes, we could have [full verb] [participial modifier] "and" [full verb]. In other words, if we depart from pattern #1 at all, we need an unambiguously clear, darn-tootin' good reason to reject the parallelism option. This can be true in an instance of "false parallelism". For more on this idea, see:
https://magoosh.com/gmat/2013/parallelis ... orrection/

Here, it's very clear that the section action, "having them decorated by local artisans" has as its subject the subject of the sentence, i.e. the same subject of the other two verbs, and so in GMAT-land, that's justification enough to make them all parallel. In the wide world of grammar, could we have other legitimate constructions? Of course we could, but the GMAT will not venture into those realms.

Is the meaning different between (A) & (C)?? --- even that's unclear. It's clear that the main subject, "The Swiss Government", is also the subject of the participle. Is "having them decorated by local artisans" a part of or explanation of "commissioning the statues"? My take is that "commissioning the statues" means they say --- "you people, make us these fiberglass cows", and then once they were made, they said to another group, the local artisans, "OK, now you folks decorate them." That's one interpretation. Insofar as there are multiple legitimate interpretations, we can't unambiguously charge (C) with the sin of "meaning change."

Does all this make sense?
Mike