I'm pretty sure this doesn't work. i.e. even in flight mode, the baseband processor is still powered and will passively listen for cell-tower requests, so presumably it can still be told to wake up?
I know its true of phones that are "off" without the battery removed - stands to reason it applies in flight mode too.
Technically this isn't true, at least not as a blanket statement regarding all phones.
Since the power button is a 'soft' switch, controlled by the phones operating system, it's possible that a phone can be compromised so that even if it appears to be 'off' it is actually still powered up and listening to the cell network, but this is in no way a 'standard' feature. The same attack vector/vulnerability is present for flight mode, a compromised phone can lie and report that the radio is off when malicious software is using it.
Removing the battery is a mechanism to preclude any possibility of your phone being exploited, and may be appropriate depending on your risk tolerance and/or threat model.
I've not seen any evidence this is the case without explicit tampering with the phone (i.e. installing spyware which then fakes the 'off' state in software).
Flight mode does not make you untraceable - it just makes your phone less useful.
If you're doing something illegal, or talking to someone about something illegal, leave your phone at home, and use your $15 dumbphone with an unregistered throwaway sim.
That's a good idea. You won't be able to stream something live anymore, though, but I guess either you record it and later upload it to websites, or some people will have to take the chance to stream it.
Put your cell phone in flight mode and use it exclusively as a PDA/music player/etc.
Let people contact you on a landline and email - more than enough.