It seems as though one of your "Apple Apps" is just crashing when it opens, which means your software has a bug in it.
I would try doing a reset: Hold the home button and the Sleep/Wake button down at the same time for about 15 seconds, until the Apple appears. (You'll be prompted to power off, just continue to hold the buttons down until the apple appears) Then you can release. Wait till the phone powers back up, then try again.
If that doesn't work, do a restore through iTunes.
I am connected to wifi. The program will stay open until it tries to connect with a caller or if I'm calling someone else and they pick up. The moment we are connected is the moment FaceTime crashes.
I have learned to turn off the iPad and turn it on again in order to connect. The only issue I find after a restart is that I cannot connect when picking up a call and only when calling out.
I have had issues with other apps crashing while in use and have reset all settings. It has not helped the FaceTime crashes. I will try the reset and then a restore if the reset does not help. Thanks!