One would imagine they are identical but this is obviously not the case.
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They can, I used to have a charger for alkaline batteries. After about 10 recharges they were useless.
It depends on the reversibility of what happens inside the battery. As an analogy, if you boil water into steam, and you catch the steam and let it cool, it will turn back into water. But if you boil a raw egg into a cooked egg, nothing can turn it back into a raw egg. Rechargeable batteries are more expensive to make, so they also make cheaper single use ones.
There are lots of completely different chemical reactions that can produce electricity.
With some of them, you can “undo” the reaction by forcing electricity through them the other way.
With some of them, you can’t.
“AA” refers to the size of the battery, and there’s an expectation that they are somewhere around 1.5 volts. There are “AA” batteries available with many different chemicals.
To be commercially successful, a battery has to either be cheaper or better than all it’s competitors. (Or have better marketing, but we’ll ignore that for now).
So there is a market for both cheaper single-use AA batteries, and more expensive rechargeable AA batteries.
(See [https://en.wikipedia.org/wiki/AA_battery#Comparison](https://en.wikipedia.org/wiki/AA_battery#Comparison) for a list of the main types of AA battery).
All batteries can be charged. However, they will explooode if they are charged above their stated voltage.
Rechargeable batteries have a switch to prevent them from charging beyond the safe voltage. That is why they cost extra. Rechargeable batteries of 1.5 volts charge up to only about 1.3
You can buy a universal charger which sets the required voltage so it shuts off before it exceeds the safe voltage. My physicist friend had one and didn’t buy batteries for ages.
DO NOT TRY THIS AT HOME.
Regular ones are alkaline batteries, cheaper but difficult to charge. Rechargeable are lithium, more expensive but easier to charge.
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