To put this thing to bed...
At the NCAA level, it's a balk & catcher's interference. R3 scores, all other runners advance on the balk & the batter is awarded 1st base on the catcher's interference.
Missed bases are considered touched until appealed. The same holds true for not tagging up. So when the 3rd out is made, you score the run. If they do appeal for a 4th out, then you wave off the run.
I will say this:
Rule #1 - Assume all ground balls on the infield are going to 1st base.
Rule #2 - You have to move.
So...
1. Make sure your starting position in C is 1/2 way between the mound and 2nd. Far too many guys get too far back and it ends up taking them out of the play at 1st. I've heard every excuse in the world (I don't want to get hit, closer to the pickoff at 2nd, etc.). Get up in there and you've already won half the battle.
2. When the ball is hit, step up, turn and face the ball.
3. Start working towards 1st, letting the throw turn you to 1st base.
There should be no reason you can't get to the far 1st base side of the working area, stopped and set BEFORE the play at 1st.
On a ball to straight away SS or that takes him up the middle, work towards the back of the mound and then across. This gets you a good angle for a pulled foot/swipe tag.
On a ball that takes the SS towards 3rd or to the 3rd baseman, work across and let the throw go in front of you.
Let the ball (or glove with the ball in it) take you to the play. Focusing on a specific object...or anything other than the ball, for that matter, will cause the play to explode on you.