What does it mean to have a mental model that 'takes into account' a higher level of reality?
it means a model that *includes* the higher level, as opposed to the former model which was entirely unaware of the higher level and which therefore believed (a fundamental, axiomatic assumption) that the ordinary level (ie the physical, manifest 3D universe) is the highest level.
The former model didn't include (ie have a place for, or an understanding of) God, because it had never experienced God. By contrast the latter (enlightened/transcendent) model does include God, because it includes the memory of the direct experience of God (the transformative divine altered-state revelation) which was lacking in the former model.
Do you directly experience this reality or merely entertain it in thoughts?
I directly experienced it firsthand, in the form of an overwhelmingly intense altered state of consciousness.
What are some details of this higher reality?
The ancient world religions all provide many accurate and detailed portrayals of transcendent reality (or altered state experiencing), in the form of myths and artistic depictions. This is precisely the subject matter of all religion - mapping and describing the higher reality. So to answer this question, just have a look at religion, but learn to interpret it as allegorical descriptions of altered state experiences. The higher reality is overwhelming and beautiful.
I think most people realize they are dependent on something. Parents, biology
Dependance on parents is a significantly lower degree of dependance than absolute, ultimate and helpless dependance on God. If your parents both die now, you would still continue to exist, and the universe would continue to exist. But if God decided to remove the veil of illusion which creates the appearance of egoic separateness, the entire universe dissolves instantly.
There are people like terrorists that commit violence and stuff but then believe they're dependent on their deity, so this doesn't seem to be unique to enlightened individuals unless we'd consider these individuals enlightened as well.
a person is enlightened (in this specific sense) when they undergo the experiential revelation of divine dependance, which leaves the individual mind permanently and profoundly transformed. This has nothing to do with daily mundane ethics, ie personal ethical conduct during everyday life. This is about intense altered state experiences and world-model transformation.
When you see behind the illusion, do you acquire non-local knowledge?
You acquire knowledge of God, knowledge of higher reality beyond ordinary appearances (beyond the appearance of a physical universe and a self/world duality). I dont know if you consider this 'non-local', it is non-ordinary.
