It makes sense that water-soluble salt when dissolved in water, they conduct electricity. Then when using the old method of the Volta Battery(using copper and zinc) with a different water-soluble salt dissolved in water, can it make electricity too? Plus, If I use a ammeter to check its current, then does all of the water-soluble salts do not go to zero?
Can the Volta Battery use a different ionic solution?
Yes you can use any soluble salt as long as it does not react with electrodes, and certainly such a battery would be able to produce current. My chemistry high school teacher had a clock which ran on salt water. See for example, https://science.howstuffworks.com/environmental/green-tech/sustainable/water-powered-clock2.htm. This technology is at least 400 years old. volta used common salt as well for zinc and copper.
Now the problem is that you can generate voltage by using copper/ zinc and salt water however one cannot predict the voltage by using the Nernst equation. It requires that the electrode dip in its own ions. Hence such batteries are theoretically difficult to deal with.