The idiom "one cell short of a battery" means "stupid." Is this a well-known idiom?

No, never heard that.

However, there are some quite common versions of this,
eg one sandwich short of a picnic.
eg one brick short of a load

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This presumably is in the same category as sayings like "thruppence short of a pound," although this one is unusual as it requires considerable electrical knowledge. How many people would know offhand what the structure of a battery is? I personally have never heard it, but I'm in the US, and these types of sayings are apparently heard more in the UK.

The meaning, as I understand it, is not "stupid," per se (as even a normal person can be stupid), but rather, indicates quite serious mental impairment, which results in intellectual deficiency and odd behavior.
No, and it itself is stupid. A single cell is a battery. You have to be one or more Xs short of a Y, where a number of Xs normally are needed to make up a complete Y.
You're technically wrong, here's why. https://batteryguy.com/kb/knowledge-base/whats-the-difference-between-a-cell-a-battery-and-a-battery-bank/
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