Also, "кажется" can be translated as "looks like". The exercises in this Russian course are often less about knowing Russian and more about guessing correctly which one among the several correct translations might be The Chosen One. Makes a rathet disappointing experience, once you actually speak the language and just want to improve your skills.
"It looks like ...", "it seems ...", "it appears ..." are all acceptable ways of expressing this sentiment. Whether Duo has all of them in its database is a different question. So don't complain -- report (using the appropriate button), and help them build their database!
Meantime, I feel your pain of having to do two extra exercises...
Well, all this reporting is actually much more annoying if you have to do it on a cell phone (not just hitting a button once), not to mention that in most cases, I'm pulling these minutes out of a busy schedule so I really don't have time to comment on that very moment. (Not today, I'm just commenting here after a long conference to wind down before finally getting to sleep.) It's just the accumulating frustration that sometimes makes me burst with at least some kind of reaction. It's not the disappointment of two exercises finding their way out of me here, it's the repeated taking of the lengthy tests in a language in which I have held several lectures on different issues, hold intensive correspondence, and from which I have translated philosophy and poetry - my actual error percentage is low but I can't always guess the minds of the creators of the tests so I could actually get to the level where I have something to study.
As a volunteer, I have an extensive personal experience, of shifting through mountains of... non-edible material, just to find a low-value coin, being a long-time admin of Wikipedia in a relatively minor language. I'd think that in this case, it might actually be possible to build some assistant software to help the team in that task - and, similarly, in the task of combining the synonyms to get the initial variants to be approved or rejected by humans. Of course, all such decisions are only as good as the humans making them, and I know nothing about the actual ability of the current team to make well-informed decisions about the plausibility of a certain sentence (it takes much more than just being a native speaker, and it takes more than just being a linguist). Yet also, as Russian is a major language, it probably should be possible to take up the active part of mapping synonymous sentences more intensively for some period, even if it would be at the expense of the junk sorting function. After all, these courses aren't THAT extensive.
I believe I have come across simple negative sentences like this one where I had to use the genitive -фамилии- in this case, but this answer was rejected here. I am sure that in other sentences with -не- the nominative was used. I am fairly sure -Кажется, это нет её фамилии- would require the genitive, but not sure that would be proper russian. Am I just confused and -не- never requires the genitive? A comment would be appreciated.
From what I've heard, Russian used to require the genitive for every negative sentence. Polish still does this BTW. Nowadays most Russian negative sentences do not use genitive but some do require it and for some it's optional, so the whole thing is very confusing. Certainly, all objects of нет are genitive, but the sentence Кажется, это нет её фамилии is not proper Russian.