Is there a simple or basic rule when to coil electrical wires or extend them if they might also serve as antennas?

Thinking mostly of those TV smart thingies powered by USB like Chromecasts, Rokus, etc.

Also what is the rule for audio cables, HDMI and such?

Read somewhere that speaker wires should be kept to minimal length (distance to speaker, not more).

Physics and maths are not my strong suits.

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If a wire is being used as an antenna, a coil can be used to make the electrical length of the wire physically shorter/more compact.

But if you’re talking about cables, like the cable that connects the antenna to the device, or signal cables such as RCAs, or any other wires such as speaker wires— these should never be coiled.

Coiled wires have certain properties that can bring noise into a system or seriously interfere with proper functioning. If you have extra length of cable, store it by running it back and forth, where it goes back over itself in a parallel fashion. Do not coil it up.

Also, avoid any hard kinks in any type of signal cables, antenna coax, HDMI, RCAs, etc.

For the most part there is no need for concern.

USB and HDMI cables are shielded, and are low voltage differential digital signals. You can coil them if you need to. I would try to get wire that are not way to long but having 4 or 5 foot extra cable will not be of concern.

Audio cables such as RCA or digital coax are about the same as far as extra length.

Speaker cables can be coiled. I have tested running speakers with a 100 foot spoil of wire between the amp and speakers and everything still worked fine. The extra resistance in the wire can reduce the power getting to the speaker but that is all. The extra inductance is relatively small compared to the speaker coils. Once again I probably would not have more than 5 foot extra wire on speaker side and amplifier side.

The only thing I would not do is coil any wires with AC Power wires,keep those separate.

My day job is an R&D Design Electrical Engineer and one of my hobbies is restoring vintage audio equipment. I am familiar with these things.

I'm not seeing any reason to coil anything other than a power cable to make the cord neater.