I take it you're referring to Beth Harmon, the protagonist of the series. There's no single chess master that resembles her, but various masters resemble her partially:
In the fact that she's female: there's only been one woman who's reached the top in chess: Judit Polgar. Two other women, Hou Yifan and Vera Menchik, come close as well.
In the fact that she'...
How was the candidate chosen?
Very simple. Money. The first to raise the $10,000 stake.
As soon as possible.
Was it some round robin format?
No. First to put $10,000 on the table gets to play the match.
Was there no Candidates Tourney at all back then?
This is explicitly stated in the Wikipedia article you reference:
From 1886 to ...
The New York 1924 tournament was effectively the Candidates Tournament, Alekhine came third, that put him at the top of the list of challengers. But before he could challenge Capablanca, he needed to raise $10,000 as per Capablanca's London Rules. That took some time. Once he had raised the amount, he then issued Capablanca a formal challenge, which was ...
Very interesting indeed. Although French, Philidor was in London for some time and virtually all the listed subscribers are clearly English, and book first edition is 1749 when he was there. It appears he played regularly at the St James Chess Club. The English were fond of clubs for a long time.
Here's a Wikipedia article with useful information: