single or double

[CoachJD]

That aslo suggests the question
3. Would the runner have been out had they thrown it to 2nd, not the cutoff.

This is not actually relevant to how to properly score the play.

For instance
Without even seeing how deep the outfielder recovered the hit ball, people say double.

Depth of the outfielder is also not relevant to how the play should be scored. Positioning of any fielder is only relevant with respect to judging if a play ought to be an error (an outfielder's starting position/how much distance they have to travel to try to catch a ball, for instance). If I put all 7 fielders on third base and the opponent hits a bunch of ground balls to the right side, they're all hits. That's just how scoring works.

 

[Nimrod]

Might have to re-open this case ...

On Aug. 2, 2012, Brendan Ryan of the Mariners hit what some described as an infield triple.

However, it was scored a single. Baseball-reference documents the play as this: ''Single to SS (Ground Ball to Weak 3B); Ryan to 3B''

See video of the play:



Also note this NCAA softball rule:

EXTRA-BASE HIT SECTION 5. a. A batter is credited with an extra-base hit when she reaches a base beyond first base solely because of her hit.

Given the precedence in MLB scoring, I'm reverting to my original position: The OP's example can be a double because the player was aggressive all the way, but if she'd slowed or stopped, then took advantage of slow play or mental error, then it's a single.