We don't know the electirc potential of the individual plates, right?
Yes, we do. Or, that depends on what we want to know. Electric potential is just the potential compared to some other point - some arbitrarily chosen reference point.
- If for example, you chose one of the capacitor plates as the reference, then this plate has an electric potential of $0\;\mathrm{V}$ and the other plat $2\;\mathrm{V}$.
- If you compare with ground as the reference, then one plate might have $3\;\mathrm{V}$ and the other $5\;\mathrm{V}$. This is not known, no, but it isn't important unless we need that connection.
If I connect one plate of a capacitor ($2\;\mathrm{V}$) to an object with electic potential $0\;\mathrm{V}$, the voltage accross the objects will be $2\;\mathrm{V}$.
Now, be accurate here. It depends on which plate, since they don't have the same potential.
If you pick the plate at a potential of $2\;\mathrm{V}$, then yes, the potential difference or voltage across this plate and ground at (if ground is $0\;\mathrm{V}$ compared to the same reference - in other words, if ground is the reference) will be $2\;\mathrm{V}-0\;\mathrm{V}=2\;\mathrm{V}$. This is the case no matter if they are connected or not.
Will there be any current flow? I know, the circuit isn't closed. But it doesn't mean anything - the voltage across objects will cuase a very short current, because the electric charge will move from one object to the other
Correct. Yes, there will be a current flowing if there is a potential difference across two connected points if it is is not restricted or resisted by anything along the way!. Charge will flow from the place of high to low potential until the potentials are equal (the higher one is lowered and the lower one is raised).
At steady conditions in a circuit there will always be equal potential along points on conductors, if there are no components in between.
If there is a component in between them, then the current might be resisted and less will flow. If - as the extreme case - the resistance is very large then it acts like the points are not connected at all and no current will flow, even though there is a potential difference across them.
You will probably say the other plate is holding the charge the plate, so it won't go to the ground even though there's a potential difference across the plate and the ground.
Not understood. Both plates hold charge (maybe), one just holds more than the other (and thus has higher potential).
The charge will never go to ground unless there is a connection to ground. Potential difference or not. What do you mean with this?
[...] voltage doesn't always mean movement of charges
True. The voltage across the two capacitor plates also doesn't mean any charge moving - they want to move (therefore the word "potential") and they will if allowed (if they are suddenly connected).
does connecting both plates of a charged capacitor always discharge the capacitor?
Yes. Because by "charging" the capacitor we mean that there is a voltage across it's plates. Because then, if the plates are connected through a circuit, current will flow.
Charge will always want to move towards lower electric potential. That is the whole point in electric circuits. So if the potential difference is destroyed, then no charge will want to flow anymore which means no current.
I hope this makes everything more clear.