Has my iPhone been hacked?
Part I: The FaceTime Call
Yesterday evening, after turning on Do Not Disturb mode for the night, my phone begin to ring (an incoming FaceTime call) with a ringtone I have never used. The caller was not on my favorites list (so the call should not have made noise since I was on DND). That caller is my co-worker at the office, and claims to have not called me (and indeed his phone has no record of the outgoing call).
Part II: The Outgoing Text Messages
Today, I noticed an unsent text to several phone numbers I do not know (and a few I do know, some of my friends) with a political message I do not support. This wasn't me sending it, so what happened?
Part III: The Suspicious Calendar Events
As detailed in this Ask Different thread, I'm having spam calendar events appear as invitations.
I have no idea what is going on with my iPhone! Have I been hacked? What can I do to resolve this problem with my iPhone?