Running to 1st
 

Batter bunts the ball. As he is running to 1st, the catcher picks up the ball and throws to 1st. The ball hits the runner.
Does the runner have to be completely physically in foul territory? Can he be running so close to the line that his left side of his body (arm) is over the line?
Or can he run so that his feet touch the chalk line?

Yes on both.

He can be in foul territory prior to the 45' running lane and unless he intentionally moves to get hit by throw there is no penalty.
Once the BR gets to the 45' running lane ct covered it.

Just because the throw hits the runner, it's not necessarily an out. The throw is not the key. If the runner is outside the running lane, and interferes with the opportunity to make the CATCH at 1b, then it's an out.

Bob

If the runner is running the last half of the distance to first base while straddling the line or touching the line and he interferes with the fielder attempting the catch at first, he's in violation and to be considered out of the lane.


Tim.

The lines are considered inside the 3 foot lane so if his foot is on the line he would be considered inside the lane.