We cannot trust software to actually disconnect as advertised. It is not in the network operator's interest. Unfortunately, it is also not in the phone manufacturer's interest to have you disconnect. Wake up, this is only a dream.
Just because there is a physical control presented to the user doesn't mean there won't be any hidden connections inside the phone still.
I think using a solid cage is the best bet.
1. If a phone is off e.g. iOS’s General->Shut Down, then can it still receive and transmit signals?
2. What is the best kind of cheap case / enclosure for a cellphone that would prevent signals from being transmitted or received? Can I just wrap a cellphone in aluminum foil and place said wrapped cellphone in a Tupperware / plastic sandwich container?
3. What is an effective way for an RF layperson like myself to detect whether or not my phone is transmitting or receiving signals while it appears to be off e.g. RF tool or measurement device?
I just want a way to know and be completely certain that “off” means “off”.
However:
1a) You don't know (because your phone can pretend to be off). You need to remove the battery (and also remove hidden batteries)
1b) some phones support NFC, which can theoretically be used when the phone is off.
2) I suggest being familiar with: https://en.wikipedia.org/wiki/Faraday_cage and your cellphone before making a decision
3) I don't know, but this would help with #2
Similar steps would have to be taken for monitoring the device to ensure the hardware switch does what it's told, same goes for the software.
https://www.insider.com/facebook-patent-photos-fingerprint-d...
Then turn off the speaker when you want to use the mic.
Or do what Snowden does and de-solder the microphone and rely on manually plugging in a mic in the headphone jack.