I used to work for a local government and, as part of my job, I had to send data to the cell network providers for analysis and return of information. For one of the providers, I had to submit the subpoena through a law enforcement website. While there, I got to look at all of the items on their menu as to what law enforcement can do (with a subpoena, back then). They can turn on your phone without alerting you and listen into conversations near your phone and can track you in any way (even if not a smart phone) and, of course, listen in on the phone and record. So, if you were a fan of the T.V. show, The Wire, all you saw there can be done.
Law Enforcement can do what they want but they would probably find your conversations boring unless you were calling up to order drugs or mutter the words: "Destroy America" or something similar. Hopefully, someone can guide you to the settings for your phone and find a setting you can use. The other thing you can do is keep your phone in a case and in your pocket when you are not using it. And try to use well-known apps from a trusted app store.