I had the same problem with my iPhone 6 in my 2014 Scion tC. The audio worked fine for music, but when I tried to use the screen for calls, it would either freeze, the buttons wouldn't be available, or it would say "No Service" even though I had full service. I tried everything that I was finding online including forgetting the car bluetooth on my phone, resetting network settings, changing from bluetooth from car to bluetooth from phone, removing the pairing and re-pairing, etc. and nothing was working. I finally found someone that said to not just reset network settings, but to reset all settings. So, I gave it a whirl and it fixed everything. The phone paired right up and everything works as it should now. The only minor issue is that you will have to go back in and redo your previous settings (ringtone, wallpaper, touch ID, passwords, etc.) It doesn't delete any data, pictures, apps, or anything like that - just general settings.
I would still delete the pairing from both the car and the phone first and then reset all settings.
Good luck!!