question about hillary's speech

I'm a english newbie, some sentences i can't quite understand in the hillary's 'exit' speech.
could anyone help me? Thank you!
A lot of questions! Thanks a lot if you would to help me!

1
To all those who voted for me, and to whom I pledged my utmost, my commitment to you and to the progress we seek is unyielding. You have inspired and touched me with the stories of the joys and sorrows that make up the fabric of our lives and you have humbled me with your commitment to our country.

Question: what does fabric mean? an underlying structure? can we use any other words intead of "fabric"?

2
Remember - we fought for the single mom with a young daughter, juggling work and school, who told me, "I'm doing it all to better myself for her."

Question: what is to better sb. to sb.? Can we rewrite the sentence in any other form?

3
I have served in the Senate with him for four years. I have been in this campaign with him for 16 months. I have stood on the stage and gone toe-to-toe with him in 22 debates. I have had a front row seat to his candidacy, and I have seen his strength and determination, his grace and his grit

Question: what does "have a front row seat to..." mean?

4
In his own life, Barack Obama has lived the American Dream. As a community organizer, in the state senate, as a United States Senator...

Question can a "Dream" been lived by sb.? what does "live" mean in this sentence?

5
Now the journey ahead will not be easy. Some will say we can't do it. That it's too hard. That we're just not up to the task. But for as long as America has existed, it has been the American way to reject "can't do" claims, and to choose instead to stretch the boundaries of the possible through hard work, determination, and a pioneering spirit.

Question: what does "not up to the task" mean?

6
We'll have to work hard to bring our troops home from Iraq, and get them the support they've earned by their service. But on the day we live in an America that's as loyal to our troops as they have been to us, we will live in a stronger America and that is why we must help elect Barack Obama our President.

Question: the support is from "hillary and other people" to "army guys", why use "get", why not use "give", or could you rewrite the sentence ? or use some other words instend?

7
Together Senator Obama and I achieved milestones essential to our progress as a nation, part of our perpetual duty to form a more perfect union.

Question: could you write it in any other form?

8
You can be so proud that, from now on, it will be unremarkable for a woman to win primary state victories, unremarkable to have a woman in a close race to be our nominee, unremarkable to think that a woman can be the President of the United States. And that is truly remarkable.

Question: what is a "close race"?

9
When you stumble, keep faith. When you're knocked down, get right back up. And never listen to anyone who says you can't or shouldn't go on.

Question: what is "get right back up." meaning?

10
Think of the abolitionists who struggled and died to see the end of slavery.

Question: what is "died to see"? had they seen the end before they died?

11
Because of them, I grew up taking for granted that women could vote.
Question: what does "grew up" in this sentence mean?

12
And to my extraordinary staff, volunteers and supporters, thank you for working those long, hard hours.

Question: Is "extraordinary staff"a metier in the American primary campaign?

13
We will make history together as we write the next chapter in America's story.

Question: "as" mean "because"? or "when" or ...?

14
So today, I'm going to count my blessings and keep on going.

Question: can lessings be counted? what does "count" mean in this sentence?