All airplane mode does is disable cell, wifi, and bluetooth transmissions, and in some phones it also disables GPS.
That's exactly what happens (Transmissions AND Receptions) just like turning off the wifi (or LAN) internet and bluetooth on your laptop, it renders a phone unreachable over the internet. And this is what needs to be done to render the phone mostly inoperative, and un-reachable by any normal cell tower, wifi network, bluetooth device, stingray, or any other method of pinging, polling, interrogating, triangulating, hacking or wiping the phone. As I said, turning the phone off OR using airplane mode is very effective in most cases (other than the situation where you have allowed wifi mode to scan for signals even in airplane mode),
Even turning your phone off does not power down the circuit board (only removing the battery will do that). The NSA demonstrated it is possible to locate powered down cell phones during the gulf war.
Somewhat correct. There is a very low power 'watchdog' latching circuit that is polling the power button intermittently, say once per second, to see if you have pushed the button and held it long enough to 'request' a boot-up sequence. But the circuit board and the cellular, bluetooth, NFC, GPS, and wifi radios are not fully powered up when the phone is off. The amount of energy required from the battery to power this watchdog is micro-miniscule and is not enough to power the phone otherwise.
The NSA has been known to be involved in all kinds of cellular interceptions, and planting malware on a phone which will cause the cell or wifi radios to remain active while the phone is in airplane mode or even turned off is possible, and it could be used on anyone, I suppose, at least in theory.
But most of us are not on a CIA or NSA or FBI watchlist so its really not a rational concern for most of us.
If anyone reading this forum is enough of an international bad actor, and a target of NSA malware planted on your $49 tracphone from walmart, well sir or madam: You are ON YOUR OWN!