If you understand how a digital switching network operates, then you realize there is no such thing as a secure phone anymore. It doesn't matter if it's a burn, or, a high end device, they're all trackable. In accordance with Federal regs., all phones now, must have GPS capability. For you protection, of course.
Yes, phones can be infected with downloadable software from whomever. (consider the topic here).
Bear in mind, every single phone has an ESN, S/N, and they also have a MAC address number. Each of these numbers can be used to track a device. And even if you're a damned good hacker, and can disable the GPS, even if your good enough to keep outside influences from turning it back on, the other numbers associated with the phone can be used to determine your location.
You're in communication a specific tower, but several other towers around are also constantly checking signal strength of your TX to determine when to switch over if your signal continues to get stronger. Same when your signal degrades, it's eventually drops you off after S/N level drop below minimum. lIt's called arbitration logic.
Now, here's something else to weigh out, even if you have a new phone, or, one which has been used before, they're still trackable. You can use them to call 911, which means, they're being monitored for signal strength, and numbers.
Every device is turned on, or, comes within a towers range, it send the info to the tower, which is relayed to a Node, which records the ESN, S/N, MAC address, GPS data, and arbitration data, and in turn, receives the authorization to use the network, or, emergency only. (911 calls), which is sent to the phone to allow calls.
If a person wishes to discuss things, I would trust no method that relays the information over wires, or air, or, even paper, now. And if you have phones on your person and wish to talk candidly, place it in a metal container that solidly closes, like a safe, a larger meatal band-aid container, etc. Either that, or physically remove the battery from the device, then wait a couple minutes before opening your conversation(s).