First part, mobile carriers: They will always know which server you are connecting to, because it’s them who establish this connection.
You’ll have to build up a proxy server, and tunnel the real destination (encrypted) through this proxy. So the carrier will only see the proxy, not the destination. Similar to TOR.
Second part, usage of the app: Since you cannot influence what the OS on the phone is logging, you’ll just have to create your own operating system and install it on the devices, or – maybe much more easy – develop your own mobile phone (hardware) which then runs any operating system you want (since you’ll have to write it on your own, too).
Please keep us informed about your progress.
solved Is it possible to hide the date and time and ip from Mobile Carrier [closed]