Using iPhone while charging and when charged Is it OK to use an iPhone 4 that is fully charged while keeping it plugged to wall outlet? 

I am worried about stressing battery too much since it is charging and discharging at the same time.

Any issues here?
None whatsoever unless you somehow drop the phone since it's attached to a cord.

The charging system on iOS devices is adaptive and only engages when the battery needs charging current. It's smart and slows down the charge appropriately whether you are using the device or not.

Put another way, the device only asks for enough power to run itself and charge if needed from the wall. The wall doesn't send too much power so there's no risk of overcharging.