Memos show Clinton Turmoil Part 4

Jackson6612Adding to the turmoil was the fact that the campaign had little strategy and no money left to seriously compete in the post-Super Tuesday contests - having (=the form having with a past participle can be used to introduce a clause in which you mention an action which had already happened before another action began) burned through $106 million before Iowa. That allowed Obama to win 12 straight contests and effectively wrap up (=to finish a job, meeting etc) the nomination.

Question: What does burned through mean?

In the end, the campaign's strategy came to reflect some of the internal turmoil, as Clinton veered (=changed course) from attacking Obama to emphasizing her personal side.

Question: What does her personal side mean?

Penn did offer some advice in March 2007 that proved on the mark - Clinton's path to victory lay with women and lower- and working-class voters.

Question: What does proved on the mark mean? I couldn't find it in the dictionary.

But by the time Clinton finally settled on that strategy to win the later primaries, it was too late.

Excerpts from the memos

"All of these articles about his boyhood in Indonesia and his life in Hawaii are geared towards showing his background is diverse, multicultural and putting that in a new light ... It also exposes a very strong weakness for him - his roots to basic American values and culture are at best (=even when considered in the most positive way) limited. I cannot imagine America electing a president during a time of war who is not at his center fundamentally American in his thinking and in his values." Strategist Mark Penn, from a March 19, 2007, memo to Hillary Rodham Clinton advising her to attack Barack Obama for his "lack of American roots."

Question: What does centre mean in the above context?