I assume spontaneous separation to ions of salt solution (or acid) requires energy to occur, right?
Where does that energy come from? Is it from the heat of the solution?
Now, if someone devised a way to draw potential energy from those separated ions, could he make this process continuous (assuming solution would draw heat from its surroundings), or would it eventually stop to work?
I assume spontaneous separation to ions of salt solution (or acid) requires energy to occur, right?
Yes, it requires energy to occur. This energy is usually referred to as the activation energy. It is a measure of the energy barrier that must be surmounted for the process to occur. In the case of salts ionizing in solution, the barrier is usually (but not always) quite small. Salts that dissolve and give off heat (exothermic) will have a lower barrier than salts that require energy input (endothermic) to dissolve.
image source: http://web.campbell.edu/faculty/nemecz/323_lect/enzyme_mech/mech_chapter.html
Where does that energy come from? Is it from the heat of the solution?
The energy comes from the surrounding environment. The surrounding molecules have a thermal energy that can be transferred through collisions with the reactants. The reactants will convert to products once enough energy has been imparted to them to cross the barrier.
Now, if someone devised a way to draw potential energy from those separated ions, could he make this process continuous
I think you're asking if the energy withdrawal can be made continuous. If so, then the answer is "yes" - at least until all of the starting material has been consumed and converted to product. This is done today, examples would include batteries, gasoline, power generators in general, etc.
When the ions of an ionic compound disolve, do not stay isolated. They form new bonds with the solvents. This makes the overall process spontaneus when a salt is soluble.
Dissociation of course requires energy. But bond formation between ions and solvent molecules release energy. This can result on a possitive (endothermic disolution, heat is absorbed in the process, like for example, $\ce{KI}$ in water. Bonds formed release less energy than bonds broken) or negative disolution enthalpy (exothermic disolution, like the one for $\ce{H_2SO_4}$ and water. Bonds formed -hydrogen bonds, stronger that ion-dipole interactions-, release more energy that is consumed by bonds broken).
Remember that if you want to know if a process is or not spontaneous, you do not have to take into acount just enthalpy, but Gibbs free energy, which is $\Delta G= \Delta H + T\Delta S$, which also takes into account entropic factors and the influence of temperature.
