- Listening is typically OK (with some exceptions).
- Transmitting is a minefield, and you could interfere with critical systems, cause outages, and get in trouble. Imagine interfering with aircraft communication systems on accident because there’s an airport nearby. Things can get pretty serious pretty quickly.
One of the things I’d like to do is build a software-defined radio (using an rpi, for example) and use it to send something like Ethernet packets over the air.
Let me start with, I am very ignorant of the pitfalls. If you can get a HAM license, they will teach you all the rules and you'll get to play in more RF space.
Otherwise, if you limit your transmissions to the WiFi bands at 1mWatt or less, you'll be fine (those are open). However, it is very difficult to do well because you are likely to generate noise on a band you are not trying to transmit on. Then the FCC will get mad at you, because you are responsible for all transmissions. Step into the wrong frequency range and you're looking at a 5 figure fine.
If you just want to play with radio hardware, so are a few other bands like 433Mhz where you can buy transmitter/receiver boards that the manufacturer certifies will not transmit outside freq. range. That's tested, so they should work well and you won't get in trouble with the FCC (the manufacturer limits the boards), the manufacturer would.
Your point about the HAM license is well-taken. That's probably a sensible next step.
I believe "leaky" transmissions are a result of the circuit design/construction (which could also be exacerbated or mitigated at the antenna level) and power being sent through the circuit and are not dependent on continuous/sporadic broadcasting. It may make it less likely to get caught, as triangulation requires an active signal. But if you bleed into ranges people care about (say HAM operators or police/military/aviation) the resources devoted to stopping you might get impressive (HAM operators because it's their hobby, the others have real government resources). Keep in mind, leaking isn't just illegal, it's also annoying whoever's transmission range you are leaking into.
Again, I would lean towards a $10 433Mhz board or a $20 ~900MHz board shipped from any electronics manufacturer before I started building my own transmitters. Or, if you're interested in transmitting using SDR and have ~$350 look into the HackRF or LimeSDR. AFAIK, they aren't FCC certified, but the HackRF in particular seems to have a wide amount of open-source use already and is probably safer than rolling your own.