1. Basically, yes. Any form of Energy can force her to go Binary. She went Binary by containing a small explosion. She went Binary by absorbing Blue Marvel's (Antimatter) High Form Energy.
2. I don't know why she couldn't. Maybe that's not what the story called for I don't know. But I do know is that throughout Marvel History AND continuity Divine Energy has always been mentioned to be one of the Highest Forms of Energy. It's not Natural or Cosmic, sometimes Magic, but it's still a form of Energy that is separated from the rest. That's why Divine Energy is so powerful, because its on par with other highest forms of Energy. The TOP Forms of Energy are: Cosmic, Divine, Magic. Of course there are levels of these.
3. She is basically a stronger version of Bishop.