"...When a battery discharges the electrolyte permeates or skins the negative or positive plate? When a battery is charged the electrolyte is electrically pumped or possibly "repelled" back out/off of the plate?"...

The electrons from a lead/acid battery come from the acid molecule splitting and re-combining.

Each element's atom desires to hold a certain number of electrons (each electron with a negative charge). However, atoms have the ability to lose a few, or gain a few, creating an electro-magnetic imbalance that is slightly positive or slightly negative. An imbalance in its charge due to an "off" number of electrons makes the atom an "ion", and they actively seek a balance.

Brute force electrolysis is when you pump electrons into water, and when the hydrogen and oxygen ionize with too many, they both become too negative and "like charges repel" so the two ions split.

Part of their bond was that they both shared an electron to balance each of their individual imbalances.

A "fuel cell" reverses that process, it places oxygen (usually from air) on one side of a negatively charged membrane, and hydrogen on the other side. When an electrical circuit is connected to both sides, the oxygen's slight imbalance pulls the hydrogen nuclei through the membrane, but the negative charge of the membrane forces the hydrogen's electrons to take the circuit path (through a motor). As many as are allowed to take these paths, then more water is re-formed.

Acid elements have "just enough" affinity for each other that they will combine to form compounds, but what they really want is to leave each other for a compound that they each prefer. Sulfuric acid is H2SO4. The SO4 (sulfur/oxygen "sulfate" group) is strongly bonded to each other, but the H2 has a weak bond that shares an electron back and forth with the sulfates.

Sulfates like iron very much, so if you pour iron filings into a bucket of sulfuric acid, the sulfates will shed their H2's (which bubble up) and it will violently bond with the iron, making iron sulfate, which falls to the bottom of the bucket.

To get the weak hydrogen bond to split and recombine (releasing or absorbing an electron), we need to find something that sulfates like "a little" better than H2, but only slightly better so the reaction is mild.

I think the two plates in a lead/acid battery are lead, and lead dioxide, which creates just enough of an imbalance to allow a charge and discharge.

As the battery is allowed to discharge (flow nearer to an electrical balance) the split-off sulfates begin coating the plates, leaving less plate surface area for a reaction, resulting in a lower voltage reading.

The freed H2's stay in solution with the water of the electrolyte, standing by to re-combine. With less sulfate and more H2 in the electrolyte, its Specific Gravity (SG) changes, it gets lighter (acid is heavier per volume than water) so stuff that used to float in it will now sink.