Chasing a Moving Target
DJI does a great job of adding new features and addressing issues as they arise while adding support for new hardware. The problem with that is for developers writing an app that supports various devices and versions of firmware, it can be a bit of a moving target.
Update: As of version 2.3.0 and up, if your aircraft or camera fail to connect once the main flight design screen has been showed you can force it to reconnect by tapping and holding the "Connected" indicator on the left side of the top status bar. After holding it for a few seconds a message will come up that says "Currently attempting to reconnect to the aircraft". This will likely fix any camera or telemetry issues.
These problems are frequently caused by the PAF (PSA on Phantom 4) switch not being in the F (P for Phantom 4) position when the app is launched. It is also likely that the DJI Go app is running in the background and attempting to connect as well. Be sure to fully close the DJI Go app by double clicking the home button to bring up the currently open apps and swipe up on the DJI Go app.
Sometimes the DJI Go app will have a pretty good hold on the connection so unplugging the cable and closing both apps will sometimes be required. Restarting the iOS device can often help as well.
The case with the camera not taking images is an especially troubling one since you can waste a whole lot of battery without noticing that anything is wrong. Make sure that the camera preview window is blinking as it takes the still images and that the grey circles are being dropped along the flight path as the aircraft executes the mission. When the non-imaging condition occurs, we have found that an aircraft and remote power cycle is needed to recover.