Indeed. They come in all kinds of sizes though. Some are pretty small.
Yeah it is, but you asked for a one-size-fits-all solution. Here it is.
That's where you start if you don't want to rely on a silver bullet and its drawbacks...
Yeah, sort of like that. They generally have signal wires for 'columns' and 'rows' and each row-column combination is indeed unique and made by shorting the respective row and column pins. Here's an example of one of those IC's: https://www.ti.com/product/TCA8418
They generally rely on the same/similar principles.