Being a (very) myopic web designer, I'm currently working on my first palette since the default design is quite challenging for my eyes. And maybe there are other users with similar issues.
So, I understand that it's possible to sell a palette to a certain stable. Am I still able to use the palette myself after that?

Is it possible to sell it to multiple stables?

Is there a store or something where I can just offer the palette and don't have to look for buyers actively?
And last but not least: What exactly happens when I select "Display Your Palette To The Public"?

I'm not an expert, but I'll answer your questions to the best of my ability:

I believe palettes are like art. If you sell it to a stable, it's theirs now, not yours. However, I do keep each palette that I make around in case something happens.

Under the same principle, I don't believe multiple people having the same palette is not allowed, but again, I'm not sure. I'd definitely ask a Mod about that one.

No, there is no store like the straw store, although that would be really cool! You have to sell it to the user personally.

Lastly, turning that to 'Yes' will let other people see your stable page with your palette applied.

Hope that helped!