I think you are right that this particular question from SS15 exam is a bit confusing. Usually it will be (and should be) mentioned in the question whether the memory is byte addressed (i.e., 1 word = 1 byte) or 2-byte addressed (1 word = 2 bytes) or addressed some other way. Here, this information is not provided. I think (but not sure) that more information would have been provided for this question during the exam time, but forgotten to include in the online paper.
Anyway, even if we assume for this question that 1 word = 2 bytes, the provided solution still is not clear as you rightly identified. For example, in this case, we will not have any bit in the memory address reserved for block offset, since the memory is addressed 2-byte wise (i.e., block-wise). But in the provided solution, there is 1 bit reserved for block offset. So as far as I can see, the question should have a main memory size of 256 bytes which is byte-addressable (1 word = 1 byte) for the provided solution to be correct. Or are there any simpler alternatives?
So I would suggest that you may ignore that question. To practice similar questions, you may refer to the exam from SS18 and WS17, where complete information is provided.