Obstruction Rule at Home Plate
 

Setup
2 Outs with runner on 3rd
Batter currently has 1 ball 1 strike

What Happened
3rd pitch is a pass ball. While the catcher goes to the backstop to rectrieve the ball, runner on 3rd attempts to steal home. The pitcher comes in to cover home plate. The batter never moves out of the batter's box. The catcher throws the ball to the pitcher to make a play on the 3rd base runner but is unable to make the take because the batter is in the way.

My Call
Batter is out for interference, no run scored.

2nd Question
What would happened if there was only 1 out? Would the batter be out and the runner still safe?

Less than 2 outs the Runner is out. 708 G

In above mentioned play:
Less than 2 outs = runner out
With 2 outs = batter is out
No runs score either way.

I found this rule in the little league rule book.

6.06 A batter is out for illegal action when -
(c) interfering 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 if runner trying to score is called out for batter's interference.

Keep reading: you are looking for 7.08g [previously cited]