Sounds like you have something on the phone that is interfering. Bad app, virus, malware, etc. You need to check the device for this stuff to see if anything is found. You can try starting up the phone in "Safe Mode" to see if it will work fine on calls and a few other things. Most apps won't work in that mode. If it works fine in there, then you definitely need to check the device for the stuff mentioned above. However, if it happens in "Safe mode" as well, then you are looking at either a full "Hard Reset" of the phone, or possibly needing to have it looked at for hardware issues.
To get into "Safe Mode" please do the following.
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.