1) yes it works. About as well as a water turbine on your showerhead.
2) you already own several tiny 'solar panels' - find any device with a temperature sensor. That's your "solar panel"
This video by an electrical engineer and pro solar YouTuber eevblog covers a system by Stanford that uses the same principle to "generate electricity at night" - https://youtu.be/Tdge8vEODeY - if you didn't try to bolt this to solar panels, it would 1/2
@skyfaller @kelbot 2/2 work BETTER (and wouldn't destroy perfectly good solar panels like the stanford one) but I can't imagine you'd be able to generate anything close to regular PV cells.
There are claims in the article that Zn4Sb3 also has some photovoltaic properties. I can't find a good source on that, but if true it MAY work better than a simple Thermoelectric generator. If it doesn't, I don't see this going anywhere outside of free energy scammers on YouTube.