First, I assume the answer key project is now dead?
Second, this sentence in the reading has me puzzled:
Fama enim reginae non erat cura.
I’m reading this as “Of course, the reputation of the queen was not a concern,” which is something of a non sequitur. I’m wondering if the intent of the sentence is to express the fact that the queen’s office was not an impediment to love she and the sailor have for one another. As I have translated it, I’m not sure what it is supposed to mean!
Here is a little advice when translating sentences from this textbook which may help to preserve your sanity:
do not try to make sense of them, they are random and often awkward and in no way related to each other. 
Your translation is good, but I would not try to weave it into any larger plots established by previous sentences.
Postermo nauta reginam relinquit et regina vitam.
I translated it as:
Finally, the sailor abandons the country and the queen [abandons] life.
Does this look right?
I think you mean “the sailor abandons the queen.”
Whoops! Yes, I meant the queen. And then the queen abandons life.
Is the sentence in this reading a common construct?
Yes, it is very common to omit the verb if the same verb would be used twice in a single sentence, especially if that verb would appear in the same form twice (as is the case here).