"So sometimes I am falling and some times I am not falling."

Glad you finally are starting to learn something.

"Does my partner know this. Does she know when you are going to propel yourself at her. Or when you are not."

Of course. You don't just do it impulsively, you build up to it, moving across your standing foot and then beyond it. It's called leading... and following

"Tell me about the ladies half of this equation. Where exactly is her body in relation to her feet. Just on one step will do. Is it a mirror image of your man."

No, we are both biased closer to our front foot than to our rear. But we do both go through substantial periods of imbalance, as can plainly be seen on any video of skilled dancers. The difference is that a skilled dancer moving backwards can maintain balance longer as they project their body than the same dancer moving forwards, because you can take your entire body weight to the very back edge of the heel, but NOT to the very tip of the toe.

"If it is she will be getting close to falling away, don't you think."

No. The relative strength of the back end of the foot compared to the front means the backwards partner stays in balance longer as their center moves past their foot than the forwards one can. This makes it easy for them to exactly match their movement to what suits the forwards partner - they have no excuse for falling away. If the lady is doing that, she's probably neglecting to support her weight from her heel, and is instead trying to move backwards from ball of foot to ball of foot.