Ask HN: Can one just assemble pieces of electronics and sell them as a kit?

In theory almost certainly yes...but if you are serious talk to a lawyer familiar with these matters. [1]

The hard part of the theory is selling. The hard part of that is identifying potential buyers and talking to them and being rejected by many, most, or all of them. The potential for rejection makes that harder than buying the components and then trying to sell them. On the other hand, buying the components and trying to sell them is the most direct route to learning what is feasible and what isn't. It is also the only way to get direct experience in the process.

Good luck.

[1]: or not. But consider that "it's not worth talking to a lawyer about this idea" can be a useful filter for the importance of ideas.

I believe so, the Arduino is already FCC approved. It doesn't need a separate approval for each retailer. Same for the LEDs etc. If you are making changes to the hardware the FCC has documentation on what is permissible for not needing a re-certification.

You can do what you like, but if the kit is intended to spy on people by sound or video or if it transmits energy through the air, as radio or WiFi signals it needs to conform to the FCC regulations and other laws that might forbid spying etc. If the kit uses AC power or dangerous high voltages and it causes a death - be prepared for possible jail time...