In regards to the Data issue, have you tried resetting the APN to default?
Settings--> Wireless & networks (More)--> Mobile network settings--> Access Point Names--> tap the overflow button (3 dots)--> Reset to default
Also within the "Mobile network settings" section, ensure "Data enabled" has a checkmark next to it.
Then reboot your phone.
As far as the sound your hearing is it about every minute or so or is it continuous? If it's every minute or so you might have a minute minder on that let's you know when a minute of your usage is gone by. You can turn it off in the dialer app settings I believe. Just go into the dialer app and hit the menu button (3 dots) and select settings from there and uncheck if there is an option for minute minder. If it's on the phone during the entire call is it while your using the phone or a Bluetooth piece to talk through?