Capacitor and Pith Ball experiment

When you connect the negative terminal to ground, why would the negative charge flow anywhere? It has to exist somewhere, and it might as well be close to the positive charge on the other capacitor plate.

You could also consider a very similar scenario in which you connect the negative side to ground before disconnecting the charging source. In this case, when you disconnect the source no charge will flow.

When you ground a terminal there will be no charge flow, as those negative charges are attracted by the positive charges of the other plate. Or use Gauss's Law, construct a cuboidal gaussian surface with 4 sides perpendicular to plates and 2 sides inside each plate (I chose cuboidal only because it's easy to explain).

There will be no flux through this surface (inside conductor $vec E$$=0$ and outside it,$vec {E}$$bot vec {dA}$) , so no net charge within it. If some charges are lost from neg plate then will be a net charge inside our surface, which can't happen.

I believe some of the other answers are wrong.

The charges on opposite plates of a capacitor do attract each other, but not as much as they repel themselves. That's why a capacitor will discharge if it gets a chance to.

So a capacitor that can discharge, will discharge.

If the side that has more elections is connected to a place electrons can go, and the other side is connected to a place that supplies electrons, some of them will move. Yes, there will be a charge at one terminal, whether or not the other terminal is grounded.

How much charge? So you need a capacitor which can do that.

"The accumulation of enough charge to detect with an electroscope requires hundreds or thousands of volts, so electroscopes are used with high voltage sources such as static electricity and electrostatic machines."

So you need a capacitor which can do that, charged that much.