Regarding sentences, are there rules that govern what gets called "parallel structure", or is it simply a descriptive term?
"Parallel Structure" is not even a descriptive term. It's a metaphor; in fact, it's two metaphors.
Parallel is a geometric term referring to line orientation in the plane. It's visual, not conceptual. There are no lines in sentences, and no visual orientation. Sentences are oral.
Structure is related to and refers to construction, frequently in a gravitational field, so support against outside forces like gravity is prominent, as well as secure fastenings. There is no gravity in sentences, nor support against it, nor stress or strain to compensate for.
Any thing composed of parts in some kind of articulation can be said to have structure.
And any two things whose 'structure' appears similar can be said to have parallel structure.
As can be seen, these are very very vague terms.
Definitely no rules. Except those promulgated by crazed writing textbook authors, of which there are plenty, so watch out.
But what it means in practice is that
- words and constructions can be repeated
this makes them look similar, so repetition counts as "parallel"
- Bill left early and I left early.
- He has a mole on his nose and he has a wart on his left earlobe.
- repeated words can be deleted if they occur in repeated constructions
this reinforces the parallel structure because that's how you reconstruct the deleted words
- Bill left early and so did I.
- He has a mole on his nose and a wart on his left earlobe.
This is all a normal part of any language. Using similar structures makes sentences easier to understand, because any structure only has to be parsed once; the next time it's recognized, it's already in working memory and can be accessed easily. On the other hand, if you know what's coming, there's not much point in repeating it. So a balance is struck, in practice.
But there are so many kinds of 'structure', and so many ways they can be 'parallel', that using the term "Parallel Structure" adds little useful information.
Especially when it's applied to writing, instead of speech, where the structures are natural. In writing, too much attention to structure usually just leads to too much structure, most of which does not contribute to anyone's understanding.