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10u game - Runner on 3rd, batter swings and misses ( or doesn't swing at a called strike/ball). Catcher steps around the right-handed batter, behind her and up the 3rd base line to run at the runner that has strayed off third. Before she gets too far, Batter steps out of the batter box at the same time and takes a practice swing, unintentionally nailing the catcher with the bat. Is this interference, what is the effect on the runner and batter? Does it matter if the practice swing was while still in the batters box?

I think this would qualify as offensive interference. Runner would be held at 3rd. Batter would be out. Note 6.06(c) below.

6.06 A batter is out for illegal action when—
(a) He hits a ball with one or both feet on the ground entirely outside the batter’s box.
Rule 6.06(a) Comment: If a batter hits a ball fair or foul while out of the batter’s box, he shall be
called out. Umpires should pay particular attention to the position of the batter’s feet if he attempts to hit
the ball while he is being intentionally passed. A batter cannot jump or step out of the batter’s box and
hit the ball.
(b) He steps from one batter’s box to the other while the pitcher is in position ready to
pitch;
(c) He interferes with the catcher’s fielding or throwing by stepping out of the batter’s
box or making any other movement that hinders the catcher’s play at home base.
EXCEPTION: Batter is not out if any runner attempting to advance is put out, or if
runner trying to score is called out for batter’s interference.
Rule 6.06(c) Comment: If the batter interferes with the catcher, the plate umpire shall call
“interference.” The batter is out and the ball dead. No player may advance on such interference
(offensive interference) and all runners must return to the last base that was, in the judgment of the
umpire, legally touched at the time of the interference.
If, however, the catcher makes a play and the runner attempting to advance is put out, it is to be
assumed there was no actual interference and that runner is out--not the batter. Any other runners on the
base at the time may advance as the ruling is that there is no actual interference if a runner is retired. In
that case play proceeds just as if no violation had been called.
If a batter strikes at a ball and misses and swings so hard he carries the bat all the way around and,
in the umpire’s judgment, unintentionally hits the catcher or the ball in back of him on the backswing
before the catcher has securely held the ball, it shall be called a strike only (not interference). The ball
will be dead, however, and no runner shall advance on the play.

(mlb rules)

This is a tough one, as it would require the umpire to exercise judgment. On the surface, it seems that no play was being attempted, rather just running the runner back to 3rd, which probably suceeded. However, if the umpire feels the catcher was attempting to make a throw to 3rd, which was hindered by the batter, the batter would be called out. This isn't "cut and dried" because it requires judgment on the part of the umpire.

The second part of the question is whether it would matter if the batter was in the box. From an absolute standpoint, no, it doesn't. As demonstrated in one of the examples above, if there's a play at the plate, the batter could still interfere with the catcher even though still in the box. In which case, the runner is out rather than the batter, with less than 2 outs.