Yes, setting the device back to factory settings will erase the phone, download a new version of the iOS via iTunes and install it onto your phone.
After that you'll be asked if you want to use an existing backup to restore your phone from, or set it up as a new device.
To rule out that damaged data from the backup are causing these problems, set it up as new device and test the call function. If it is working, restore from the last backup you made. If all apps are part of your media library on your computer, iTunes will install everything back onto your phone, apps and their settings included.
Check this article about backups as well and make sure to backup before you start.
About backups in iCloud and iTunes