EXAMPLE : At Shiprock, New Mexico, a perennially powerful girls ...

At Shiprock, New Mexico, a perennially powerful girls high school basketball team has become a path to college for some and a source of pride for a community where the household incomes of 49 percent of them are below the poverty level.

C. where 49 percent of the household incomes are
D. which has 49 percent of the household incomes

The difference is one of meaning, not of grammar (choice D is perfectly grammatical). What choice D actually means is that this one little community in N.M. has 49 percent of ALL the household incomes below the poverty level (i.e., in the entire country, or whatever is the whole universe of reference). That's unlikely, to say the least, and, more importantly, it distorts the clear meaning of the original sentence (you're never allowed to do so unless the original is nonsense).

The other thing that doesn't make sense in choice D is '49 percent of the incomes'. It's not 49 percent of a bunch of figures on an Excel spreadsheet; it's supposed to be 49 percent of the households (or of the households' incomes).

TIPS : Similar to VS Just as

Although fruit can no longer grow once it is picked, it continues for some time to respire, taking in oxygen and giving off carbon dioxide, similar to the way human beings breathe. 

(A) similar to the way human beings breathe 
(B) similarly to human beings who are breathing 
(C) just like the breathing of human beings 
(D) as human beings when breathing 
(E) just as human beings do when they breathe

"Like" and "similar to" mean much the same thing. "Just" before "like" means "exactly". So the difference between "just like" and "similar to" is a matter of degree. 

You are similar to your father. You and he have some similarities. 
You are just like your father. You and he are exactly the same. 

But for this SC item I would not choose "similar to" or "just like". The best response here is E. The sentence is pointing out that fruit respires by taking in oxygen and giving off carbon dioxide and that humans breathe in the same way, so the conjunction "as" is appropriate.

EXAMPLE : Embryonic mammalian circulatory system ...

A peculiar feature of the embryonic mammalian circulatory system is that in the area of the heart the cells adhere to one another, beating in unison and adopting specialized orientations exclusive of one another. 
(A) beating in unison and adopting 
(B) they beat in unison while adopting 
(C) beat in unison, and adopt 
(D) beating in unison yet adopting 
(E) even though they beat in unison and adopt 

a couple of comments: 

* you said 'the correct answer'. is (a) actually the official answer? i think (d) is the better choice, for the reasons outlined below. actually i like choice (f), my own version (see the end of this post), but (d) is the best of the choices given here. 
is this a real gmatprep problem? if so, i'm surprised the writers didn't compose a correct answer closer to the one i've labeled (f) below. 

-- 

(a) 
parallelism & mechanics are ok, making this the second-best of the choices here, but this one misses the point: the cells beat in unison, but they adopt orientations exclusive of one another. these facts are diametrically opposed to one another: the first talks about cooperative action, the second about completely independent action. that's a striking contrast, one that certainly deserves a CONTRAST TRANSITION such as 'but', 'yet', 'although', etc. 
not 'and'. 

(b) 
two ways to view the grammar here; either way it's wrong: 
- poor parallelism (your interpretation) 
- comma splice: you have an independent clause (i.e., something that could be a standalone sentence by itself), then a comma, then another independent clause. that's not allowed. 
note that this choice would produce a perfectly good sentence if the comma were replaced with a semicolon. 
also note that 'while' is an acceptable CONTRAST TRANSITION, although good transitions don't rescue a choice with bad grammar. 

(c) 
i see your point about the singular 'feature' referring to 3 different parallel components, but i don't think that's the issue here (one could conceive of the 3 different actions described as a single feature, if they're related closely enough). but that argument is moot, as this choice suffers from the same problem as (a): no CONTRAST TRANSITION to convey the intended meaning effectively. 

(d) 
all the grammatical advantages of choice (a), but with a proper CONTRAST TRANSITION. this one gets the thumbs up from me. 

(e) 
this isn't nonparallel, but the CONTRAST TRANSITION is in the wrong place: it's placed between 'adhere to one another' and 'beat in unison'. that's not the right contrast; the correct contrast is between the beating in unison (cooperative action) and adopting specialized orientations (individual action). 

EXAMPLE : A collection of 38 poems by Phillis Wheatley ....

A collection of 38 poems by Phillis Wheatley, a slave, was published in the 1770s, the first book by a Black woman and  __________________________________________________

C. the second one only published by an American woman 
E. only the second published by an American woman

E.

C changes the meaning , it means that American Women published no other book , but this one. The E puts 

the meaning clearly saying that it is the 38 poems was the second to be published by an American Women.

Notes

notes-mind-only

NOTES : Mind the ONLY/FIRST ....

The "only" position shift changes the meaning of the original setences.

"The following sentences should make the meaning differences clear:

Only Linda ate the pizza today. (Nobody else; only Linda.)
Linda only ate the pizza today. (Linda didn't cook it or buy it; she only ate it.)
Linda ate only the pizza today. (Linda didn't eat anything else today; only pizza.)

Linda ate the only pizza today. (There was only one pizza, and Linda ate it.)
Linda ate the pizza only today. (Linda didn't eat the pizza yesterday or before;

only today; OR, Linda didn't eat the pizza until today.)
Linda ate the pizza today only. (Linda didn't eat the pizza yesterday or before; only today.)

The rule of thumb is this: put only as close as possible to the word it should modify.

Look out for very words like ONLY, FIRST, etc. They can contribute to change in meaning in a subtle way.

Example:
example-quetzalcoatlus

example-victoria-and-albert-museum