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You are measuring Voltage, not charge. These are two different things!
(if anything, charge is more related to current, Amps, than voltage. Combined voltage and Amps form the used power, which integrated over time will give consumed energy - which many think is the same as charge)

It is not uncommon that batteries regain some voltage when not in use; quite usual in fact. This is as when in use the load will decrease the peak voltage, all depending in resistanses in battery (-ies) and load resitanses. Unloaded, the battery will go back to peak voltage, a process that takes some time.

- this can also be explained from a battery intrisic point of view, with chemical balances.

To some of the other aspects
- a "small" solar panel can be directly connected to a "large" battery, that is no problem. Again, Solar panel peak voltage will decrease due to the low battery resistance. Regulators are used to a) see to that peak voltage is below boiling point and b) convert peak voltage to useable energy at lower voltage.
- to tap 12V for house use from one of the batteries seems a simple solution. Probably the best battery should be used for this. And solar panel mainly connected to this one - depending on your consumption.

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