This question was asked a while ago, but never got an answer. The comments focused on how a goal of "getting into a top 6 PhD program" followed by a "top 30 professorship" was a potentially unhealthy goal. I agree with that, so this answer is aimed at anyone applying to grad school, even beyond the "top 6." Let's start with question (a), regarding personal statements.
Yes, you can use your personal statement to explain relevant personal hardships, how they affected your performance, what you learned from them, and how you've grown.
Here is some general advice about grad school applications, from Swarthmore. Their advice item (2) is to do as well as possible on outside measurements like the GRE, REUs, study abroad, and Putnam exam. Their (3) is to take as many challenging math courses as possible (it sounds like the OP did this). Challenging courses and good letters of recommendation matter more than perfect grades. Their (5) concerns applying for grants to fund your PhD, (6) is about letters of recommendation, (7) is about your personal statement, and (8) is about emailing professors at places you apply.
The advice from Swarthmore is backed up by web pages of various PhD programs, e.g., this one from UMD, previous MO questions, MSE questions, and advice on academia.SE. The idea that it's ok to have some Bs, especially in hard courses, appears in those links and is confirmed here and here.
Let's turn to question (b) regarding how graduate school admissions committees view personal hardships.
Yes, done right, your history of overcoming a personal hardship can become a strength in your application.
The last link above also includes advice to use your personal statement to present yourself as a "whole package." A candidate can use their personal statement to strengthen their application if they explain (briefly) the personal hardship and how they learned from it and bounced back from adversity. You can find more advice here regarding the personal statement and using it to tie together your record. There have also been previous advice threads about using the personal statement. The general theme is that, if written convincingly, the personal statement can definitely help you, especially if it's related to your motivation, determination, grit, resilience, and current ability to succeed in their program. The story in that thread (and responses to it) show that for sure the personal statement and overcoming hardships, can play in your favor as the applicant.
The advice at all these sources consistently says to keep the story short and to the point. Aim for around two pages for the personal statement. Since letters of recommendation are consistently put among the top criteria (whereas, personal statements are not), it might be wise to talk to at least one letter writer about your concerns that the grade dip will harm your chances of being accepted, and to explain to them what happened. You can't really tell them how to write their letter, but if they agree with you during that conversation, odds are that they will add a sentence or two backing up your story and expressing their confidence regarding you despite this previous hiccup.
Lastly, I want to re-emphasize the point made in some of the comments that setting goals like "being accepted to a top N university" is not wise for mental health, and is not necessary for career success. Certainly it's true that there's a prestige bias in mathematics (happy to share links to published research that proves this if you want). However, the advice on MO, MSE, and academia.SE is consistent on the point that it's better to choose a field of study that you love (instead of whichever you think might best help you get a job), choose an advisor you have a good relationship with (instead of the most famous / influential advisor), and choose a graduate program where you can be fulfilled, productive, and happy (e.g., taking into account the location, culture, other students, your romantic partner, etc.) instead of whichever is the most prestigious. In math, we're so used to optimization problems, but in life, it's important to optimize on a number of different fronts simultaneously (and, honestly, for happiness, it's better to take an attitude of "satisficing," e.g., "this job might not be the best I can get, but it's good enough for me and I'm happy with it"). Constantly climbing and defining your self worth in terms of something as fickle as external rankings of your university, is not a recipe for a happy life. Good luck with your applications, PhD experience, and life!
