Are my analogies correct for current, voltage and potentials?

Hello! Not at all true! Why invent what is described in the physics textbook? Voltage and EMF are described in this article. In short - voltage is a quantitative characteristic of the work that needs to be done to transfer charge from one point to another (from plus to minus for example). The current strength is not speed, but the number of charges, i.e. how many of them passed through the cross section of the conductor per unit of time.

Let me remind you that from mechanics, speed is the first derivative of the path, in time. those. what distance was traveled per unit of time (passed 100 meters in 2 minutes).

Potential, by definition, is a quantitative characteristic of the work of charge transfer from a certain point to infinity. In this case, voltage is the DIFFERENCE of potentials between something.

Although in part you are right - voltage is what makes the current arise.

But what does it mean “on the example of batteries”, because these concepts are the same everywhere. The potential does not end there, if you mean that the voltage on a charged battery may be slightly higher than on a discharged one - it is only without load, under load this difference will be much larger. But this does not mean that the potentials have decreased, it says that the internal resistance of the power source has increased and part of the voltage drops on it, and the EMF remains almost unchanged.

Regarding the resistance, you correctly said, not speed, but what prevents this amount of charges from going through. It is as if you would let a crowd of people in a wide corridor empty, and in a crowded with different boxes, in the second case, people would not walk along the entire width of the corridor, but would crowd around the aisles, thereby less number would pass in the same time of people