The question does not make much sense and I think you've gone about as far as anyone can go.
A) at least one character changes
Not necessarily! In any tree, of interest, it will be true that something will have changed but in theory, the only thing that separate two nodes is time. It is not impossible that your teacher was hoping for A to be the correct answer but it is not IMO. It is also very much possible that the only change in between two nodes relate to synonymous mutations (and other mutations that has no effect on the phenotype), hence not causing a change in any character fo interest.
B) all organisms die
Well, most likely enough time separate the two nodes that all organisms that were represented in the ancestral node are dead but of course they have reproduced, so that we actually have another node that descend from it.
C) Nothing can happen between two nodes
As you said, they evolve. So, things happen!
D) Monophyly, Paraphyly, Polyphyly
As you said, those terms make no sense here!
E) None of the above
If there is any intuitive answer to the question what has happened between two nodes is time has passed. I think the answer your teacher was expecting here is E. But really that's a pretty poorly written question IMO.