Self-restraint is not one of Beelta's many strengths, but the knowledge that the weird demon might be her only chance for breakthrough made her restrain herself. There is simply too much at stake. She had to take things carefully because she doesn't want to lose her chance.
So eating the weird demon became the very last option. She would try everything she can do to get that access to chaos and if it doesn't work, she will then eat Aeternus.
She decided to question him first and figure out where, how, and why he got the power. But she knew that wasn't going to happen easily. She couldn't walk up to him and ask him about his power and receive answers.
No demon will do that in their right mind. This weird demon is surely not going to spill the beans by being asked politely. The fact that you're asking a question means you need the answer, which means the answer is important to you. Demons will capitalize on that and try to get benefits from you.
