The confusion here is from the initial poor description of how a battery works.
A battery consists of three things: a positive electrode, a negative electrode, and an electrolyte in between. The electrodes are made of materials that strongly want to react with each other; they are kept apart by the electrolyte.
The electrolyte acts like a filter that blocks the flow of electrons, but allows ions (positively charged atoms from the electrodes) to pass through. If the battery is not connected to anything, the chemical force is pulling on the ions, trying to draw them across the electrolyte to complete the reaction, but this is balanced by the electrostatic force-- the voltage between the electrodes. Remember-- a voltage between two points means there is an electric field between those points which pushes charged particles in one direction.
When you add a wire between the ends of the batteries, electrons can pass through the wire, driven by the voltage. This reduces the electrostatic force, so ions can pass through the electrolyte. As the battery is discharged, ions move from one electrode to the other, and the chemical reaction proceeds until one of the electrodes is used up.
Thinking about two batteries next to each other, linked by one wire-- there is no voltage between the two batteries, so there is no force to drive electrons. In each battery, the electrostatic force balances the chemical force, and the battery stays at steady state.
(I kind of glossed over what it means for two materials to "want" to react with each other. Google "Gibbs free energy" for more details on that. You might also google "Nernst equation.")
You have the right idea. If you add a diode in series, you can only charge the capacitor, and wait for self discharge to occur. Or if the diode is reversed, you can only discharge it (or charge it with reverse polarity), and once again wait for self discharge.
An exception to this would be to have some other connection between the diode and the capacitor.
So long as the battery is connected, the capacitor will just remain charged. Once the battery is removed, if there's some closed loop path between the plates of the capacitor, then the excess charge on one side of the capacitor will use the closed loop to balance out the charge. Excess electrons from the negative terminal of the capacitor will move towards the positive plate of the capacitor to allow charge balance to occur.
Best Answer
Consider an analogy
Consider two water tanks with first tank having a higher water level in it. These tanks are connected to each other as shown in figure.
Case 1: The interconnect is a water filled hollow pipe: The water will flow from left tank to right tank.
Case 2: The interconnect is a hollow pipe filled with ice: There won't be any water flow.
In both cases, the pipes are filled with same molecules (\$H_2O\$). But the flow will happen only if the molecules are free to flow. Bounded molecules (as in ice), won't contribute to flow.
Electrons are like these water molecules. They will contribute to flow (current) only if they are mobile. So the excess electrons from negative plate to the positive plate will flow only if the interconnect have free (mobile) electrons in it.