1) There is a risk of failing the test.
Perfectly normal. It presupposes that failing the test would be undesirable, and asserts that it might happen.
2) There is a risk to fail the test.
This sounds like a non-native speaker error to me. If I heard it, my best guess would be that the speaker meant "There is a risk of failing the test." (Context might suggest a different interpretation, though.)
While Britons seem to oppose the use of the infinitive after the noun "risk", in the American English such a construction seems to be acceptable and comprehensible.
I am American, and neither accept nor comprehend your sentence, so I think you're mistaken about that.
"are you going to choose to take the risk to vaccinate and get this long-term chronic illness"
This is by a non-native speaker (see https://www.cbsnews.com/news/minnesota-measles-outbreak-vaccine-misinformation-targeting-somali-americans/), so is not a great example of what Americans accept or comprehend. That said, the idea being expressed is a complicated one, and I could well imagine a native speaker also stumbling a bit over how to express it (especially since news interviews can be stressful). In context, the meaning seems to be roughly "Are you going to vaccinate your child against measles, believing that this creates a risk of autism?"
"He is taking a great risk to give me information about the work they are doing"
"it could really be a risk to put themselves out there"
"Kassimu and Lemmy maintain that it is not a risk to keep the local stations on air"
"So did you feel like you were taking a risk to speak to this guy who's tattooed from head to foot"
"But it's always a risk to have a jury trial."
These all seem more-or-less fine to me, though in the "taking a risk" examples I would have preferred "by verbing" or "in verbing" rather than "to verb".
In these examples, note that the verb phrase is not a complement of the noun risk; for example, it's not *"it could really be {a risk to put themselves out there}", but rather "it {could really be a risk} {to put themselves out there}", such that it's synonymous with "Putting themselves out there could really be a risk". (It doesn't indicate what the risk is of, though perhaps the context makes it clear.)
Also note that this is a somewhat different sense of the noun risk, in that it's being applied here to the risky action, whereas in your first example it's being applied to the probability of the undesired result. (This sort of flexibility, where the same word can be applied to multiple different elements of a situation, is pretty common in English; for example, "vegetarian" people eat "vegetarian" food, a "happy" occasion makes participants feel "happy", and so on.)
"Stewart found Bundy, 69, remains a danger to the community and a risk to flee"
This one sounds wrong to me, but since it's paraphrasing a judge's order, maybe it's just legalese? (Lawyers have their own idioms.) I would have said something like "Stewart found that Bundy, 69, remains a danger to the community, and that there's a risk he would flee".
"A challenge to create and a risk to consume"
"He thought it was a risk to ask for her number"
"and she knew then that it was a risk to attend Bonnaroo"
These sound fine to me.
Now, if we take a sentence "It was a risk to attend that meeting", and change it to "It was a risk of attending that meeting", the meaning of the sentence would also completely change.
Agreed.
It was a risk to attend that meeting.
To attend that meeting was a risk.
These are fine.
There was a risk to attend that meeting.
I don't know what this is supposed to mean. Do you mean "There was a risk in attending that meeting"?
It was a risk to fail the test.
To fail the test was a risk.
These are grammatically fine, but the meaning is odd: they presuppose that someone is intentionally failing the test (to achieve some desired outcome), and state that it's merely a "risk" that some undesired outcome may result (as well or instead). It's possible to imagine such a situation, but it's definitely not how tests usually work!
There was a risk to fail the test.
I don't know what this is supposed to mean.
Best Answer
This comes down to the difference between "ways of ensuring" and "ways to ensure", which is a subject that has already been discussed on this forum.
In a case like this, where there are multiple ways and there are no possessives involved (no "my ways of doing" or "their ways of doing"), these are just two ways of saying the same thing. Some people say there is no difference in meaning. Those who say there is a difference say that "ways to do" suggests that one is better than the others or that what is being done is more purposeful, whereas "ways of doing" is more neutral.
The difference becomes clearly visible when way is singular. "This is the way to ensure..." is much better than "This is the way of ensuring...". Conversely, when possessives are involved, "my way of doing" is much better than "my way to do", which is downright wrong.
But neither of these considerations apply in the example, so actually revision (C) can be made to the sentence, but none of the revisions must. It seems a strange way to set a question.