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1) Runner on first, batter hits hard grounder to outfielder who throws to 2nd in time to force out runner from first.

Variation: runner on first, batter hits fly ball to outfield, runner stops 1/2 way to second to see if caught. Ball is not caught but outfielder throws to 2nd before runner from first arrives for force out.

I've always scored these as FC, but reading the MLB rules confuses me:
10.05(a)(4) - credit a base hit when batter reaches first base safely on a fair ball that has not been touched by a fielder that is in fair territory when the ball reaches the outfield, unless an error.

10.05(b)(1) - not credit a base hit when a runner is forced out by a batted ball, our would've been forced out except for a fielding error.

10.05(b)(3) - not credit a base hit when a pitcher, catcher or any infielder handles a batted ball and puts out a preceding runner who is attempting to advance one base... (interesting it specifically excludes when outfielders put out preceding runners)

I'm interested in your opinions.

I have always scored that as a FC as well, not really focusing on whether the ball is a ground ball or line drive. NCAA softbball rules do not have the qualifier that it must be an infielder making the play, but does have the reference to the ground ball:

A fielder’s choice is credited in the following situations:
14.7.1 To a batter:
14.7.1.1 When a ground ball is put in play and any preceding
runner is out on the hit or would have been
out had no error occurred.
14.7.1.2 When a ground ball is put in play and the lead
runner is safe, but the batter would have been out
had the initial play gone to first base.
14.7.1.3 When a ground ball is put in play and any preceding
runner, who is forced to advance, is called out
on an appeal for missing the first base to which she
was advancing.

Of course the when the fly ball reaches the ground without being caught (assuming no error), does it automatically become a ground ball??

10.05(b)(1) determines both of the variations. If the preceding runner is put out due to a force play, then the batter is scored with an FC. 10.05(b)(3) only comes into play when the runner is not forced.

That makes sense, but then I wonder why they have rule 10.05(a)(4)? Why does it matter if the ball reaches the outfield?

But could the outfielder have gotten the runner at 1st? How can it be a fielder's choice if the outfielder couldn't have gotten the batter in the first place?

Seems to me it's a hit... The runner from first to second was a casualty of the hit.

Whether the outfielder could have gotten the out at first is actually irrelevant. This rule actually robs the batter of what would otherwise have been a hit if no runners has been on base.