Sorry to hear about your iPhone issues.
First thing I would try is a simple reset of network settings. To do this, go to settings > general > reset > reset network settings. The phone will reboot, you will not lose any saved data apart from saved wifi info and VPN settings if you added any.
If this doesn't help, I would suggest restoring the phone through iTunes. Simply connect via USB to your computer, select the iPhone from the left, and click restore. You may need to update the OS if you are not on the most recent version. You will then be prompted to restore either as new device or from backup, I'd try from backup first. Once complete, test out the phone and let us know if it helps!
The pause time seems to flucuate. During the day it only take 1-2 seconds to connect a call, but late at night say 10:00 PM, it takes like 15 seconds to start ringing. What would be causing it? The volume of calls the tower is processing?