You can also learn pidgin Swahili. (This was a “free tip” offered to me by a guy taking collections at a Salvation Army dropoff site. He and his daughter developed a version of Swahili so that no one could eavesdrop on them. According to him, the CIA knocked on his door asking about it just a couple of weeks after they started. So… the CIA can tap your phone, computer, etc. but they can’t read Swahili.)
There are portable communications devices that do indeed allow monitoring whilst they are turned off.
I use one every day from the user end - not the monitoring end, and whilst these are not mobile phones, the technology is so similar that it is no stretch of the imagination at all to believe this is possible, heck, some versions also broadcast their precise location, off or on.