If the only runner on base is on third I would run right at the runner to force her back and throw the ball to the pitcher in the circle.When the pitcher has the ball in the circle, runners have 2 choices; go back to the base or proceed to the next. If they do neither, they can be called out with the look back rule.

Consider throwing the ball back to the pitcher and ignoring the runner, unless the runner makes a mistake and opens herself up to be put out. I've seen a catcher charge the runner then throw the ball back to the circle, leaving home uncovered and the runner ran in far an easy run. I'd suggest ignoring the runner, or at least appearing to ignore the runner, but be ready to nail her if she makes a mistake. This conserves energy and keeps the runner from trying to disrupt the pitching rhythm.

If its your only runner, the catcher should charge down the line to pin the runner on base. For this
to be effective you must have a catcher disiplined enough to hold the ball until the 1st baseman is
in position to cover the plate. Do not encourage your pitcher to cover home.

Depends on how big a lead she takes. Just always be aware of the runner on third with every pitch. A quick throw back to the pitcher would be fine.

First off the opposing coach is hoping that the catcher will throw the ball away. Second it upsets the rythym of the pitcher to have the catcher keep running the runner back to third. Best bet is to quickly get the ball back to the pitcher if the runner is taking a short lead. If she is getting a big lead than I would run her back but you need to be certain that the 1st baseman is covering home if no one is on 1st

As most of the post address, it really depends on how far out the runner gets and her quickness. Constantly running a runner back that has no intention of going can be very tiring for a catcher, especially if you are playing tournament ball and have several games throughout a day. However, you certainly don't want the runner getting to far of a lead without you keeping her honest. One of my players is very fast and aggressive and has been able to score us alot of points by capitalizing on a pitcher and or catcher that has gotten a little to lazy and stealing home when the catcher throws back to the pitcher. One thing that I teach our girls is to run hard for a couple of steps and as soon as they turn, get it back to the pitcher so they are not to far off of the plate. I do not advocate the "fake" throw because it provides the opportunity for the person throwing to lose control of the ball and have it slip out and roll across the ground. I

One of my favorite scoring memories is one where the coach encouraged the runner to play with the catcher and got her to chase her back to 3B. The catcher threw the ball to the pitcher leaving home open for an easy run.

throw it back to the pitcher quick and if she is still off the bag and not going back or going back slowly with her head down and not paying attention, tell the pitcher to nail her