"One is getting sick."
Translation:On tombe malade.
Context is necessary here, possibly. Could it not be "Un devient malade."? "One" what? As a native American English speaker, we would not say this generically. If you were looking at a group of puppies, for example, you might exclaim to someone with you, "Oh, no! L:ook! One is getting sick." If this was the case, you wouldn't use "on", would you?
The tricky part with on is that you can use it literally everywhere. It's indefinite, so yes, you can use it in your context. You can also use it we speaking about yourself, people in general...
Now, if you want to use another word, it's still possible. You can't use un alone. I mean, you can only in the construction One is getting sick and the other not = Un devient malade et l'autre non, but that's not the case here. You can use L'un d'eux = One of them for instance.
On my mobile app, the question is "One is getting sick," and the only possible answer I was allowed that made any sense was "Nous tombons malades." There was no "On." Can this be correct?
Nous is first person. The only case of passive use I can think of is "Nous sommes Lundi." Is this something like that?
aka One. No one uses one to mean we. Not correctly anyway. One/someone means anyone. We means the person saying it and at least one other person.