I thought that in B, "which" always must refer to the previous name, that is Nixon, and for this reason it would be incorrect. But in fact, OA is B.
Can any instructor explain?

Although she had been known as an effective legislator first in the Texas Senate and later in the United States House of Representatives, not until Barbara Jordan’s participation in the hearings on the impeachment of President Richard Nixon in 1974 was she made a nationally recognized figure, as it was televised nationwide.
A. later in the United States House of Representatives, not until Barbara Jordan’s participation in the hearings on the impeachment of President Richard Nixon in
1974 was she made a nationally recognized figure, as it was
B. later in the United States House of Representatives, Barbara Jordan did not become a nationally recognized figure until 1974, when she participated in the hearings on the impeachment of President Richard Nixon, which were
C. later in the Untied States House of Representatives, it was not until 1974 that Barbara Jordan became a nationally recognized figure, with her participation in the hearings on the impeachment of President Richard Nixon, which was
D. then also later in the United States House of Representatives, not until 1974 did Barbara Jordan become a nationally recognized figure, as she participated in the hearings on the impeachment of President Richard Nixon, being
E. then also later in the United States House of Representatives, Barbara Jordan did not become a nationally recognized figure until 1974, when she participated in the hearings on the impeachment of President Richard Nixon, which was

If i am not wrong, which here modify its the "impeachment of President Richard Nixon", because is a possessive noun.

I think that you are wrong.
Which here is modifying "hearings".....and for this reason I suppose that B is correct

yes.

here is a detailed post on exactly when you can do that:
post31162.html#p31162

For this one, IMO,
Since 'hearings' is plural, so we can eliminate A(was), C(was) and E(was)
Then we read B&D, and D is awkward in saying 'then also later', so, got B
I reckon this method is pretty fast^^

correct on (c) and (e); incorrect on (a).
(a) is a backward construction; the subject of "was" is "she", which comes afterward.

the easiest way to detect backward constructions is not directly, but, rather, just by figuring out that the noun(s) that precede the verb cannot be the subject.
here are four really simple examples (all are correct):
1) there is a car in the driveway.
2) there are two cars in the driveway.
here, there's nothing in front of the verb that could even be considered as a subject -- the only word in front of the verb is "there", which is neither a noun nor a pronoun. therefore, the subject is "car"/"cars".
3) on the table was a cell phone.
4) on the table were two cell phones.[/i]
here, "on the table" is a prepositional phrase, and so is ineligible to be the subject. therefore, the subject again must follow the verb (since nothing in front of the verb is left to be considered), and so the subject here is "cell phone(s)".

choice (a), although it contains other errors, is another one of these backward constructions.
"participation", "impeachment", and "nixon" are all trapped in prepositional phrases, so none of those can be the subject. therefore, the subject must be "she".
i.e., "was she..." = verb + subject.
it probably looks awkward to you if you aren't a native speaker of english (although this construction should be plenty familiar to anyone who *is* a native speaker of english), but you should know that it's legitimate.

Pls, help

in A, "she" can not refer to " Barbara Jordan’s" .

Is that thing right?

Why B is wrong?

yes, you are right that "she" cannot refer to "Barbara Jordan's", as a subjective pronoun cannot refer to a possessive noun..

as for your second question, i cannot explain why B is wrong. it is pretty clear from the discussion that B is the correct answer, so i'm a little baffled as to why you are asking why it is wrong..

_________________
Tim Sanders
Manhattan GMAT Instructor