Foul Tip or No Foul Tip? That is the Question

 
1. With no outs and the runner (R2) on second base stealing, the batter (B1) swings at the 0-2 pitch. The bat tips the pitch. The tipped ball hits the catcher's mask and is then properly caught by the catcher in his glove. The catcher then throws to 3rd base to retire the stealing R2. What is the call:

A. B1 is out, since the catcher secured the third strike before it struck the ground.
B. Foul ball, so B1 remains at bat with a 0-2 count
C. R2 is out on the tag
D. R2 returns to 2nd base
 
Call
A foul tip is a pitch that is tipped by the bat and then goes sharply and directly to either of the catcher's hands and is properly secured. A foul tip is a strike and a live ball.

In #1, the ball did not go directly from the bat to either of the catcher's hands (it first went to the catcher's mask) -- therefore it is a foul ball -- and answers B and D apply.

2. With no outs and the runner (R2) on second base stealing, the batter (B1) swings at the 0-2 pitch. The bat tips the pitch and then goes directly to the catcher's glove, but then falls out. Before it touches the ground, the catcher traps the ball against the top of his foot, and then finally secures it in his bare hand. R2 stopped running during the steal, so the catcher throws to the shortstop who tags R2 who is standing between 2nd and 3rd base. Which of those four statements above are true?

Call
In #2, the ball did go sharply and directly to the catcher's glove. After that, the ball was properly secured - so the pitch is a strike. The ball remained live (so R2 is out on the tag) and answers A and C apply.