Did Moses see an actual burning bush?
Hallucinations may occur secondary to tumors or seizures involving the occipital, parietal, frontal, and temporal lobe, or arise secondary to drugs, toxic exposure, high fevers, general infections, exhuastion, starvation, extreme thirst, partial or complete hearing loss including otosclerosis, and with partial or complete blindness such as due to glacoma ... For example, tumors or electrical stimulation of the occipital lobe produce simple hallucinations such as colors, stars, spots, balls of fire, flashes of light.
Source: http://brainmind.com/Hallucinations88.html
Next, Moses supposedly heard the voice of God, not coming from within his own head, but from somehwere else. (Or God wrote the commandments on the two tablets himself) A certain type of brain injury can cause that too, as can schizophrenia. Stress can also cause auditory hallucinations, including stress due to sensory deprivation. Moses was alone, so we don't "know" what his sensory input was. Another potential cause is a milder condition, in which ordinary sounds (such as the wind rustling through a shrub high on a mountain) can be misinterpreted in the brain and turned into full-fledged vocalizations from outside the mind. And "The most common type of auditory hallucinations in psychiatric illness consists of voices" so the likeliest thing for Moses to hear in this state would have been one or more voices. Since he was alone, naturally he had nobody to attribute the voices to other than God. Someone experiencing the same thing today might make the same mistake (unless they had just ingested a psychogenic plant!)
Source: http://www.psychiatrictimes.com/schizophrenia/content/article/10168/1534546
So my verdict on Moses: some kind of hallucinatory experience, from any number of causes, is much more likely than God performing a miracle and then talking to him. Moses most likely did not exist, but ancient people would have been aware of the phenomenon of seemingly sane people having hallucinations that they interpret as coming from a divine source.
Dreams
Dreams likewise seem to have an external origin. Even the few people who claim to be able to do "lucid dreaming" or otherwise control their dreams admit they work very hard at it. For the rest of us, dreams are foreign invaders into our experiences, spinning out stories that can be the cause of great distress. Like hallucinations, our reality-tester in our brain is out of commission and after the fact has no basis for knowing what was real. Everything seems real in a dream. I do agree with dream interpretation as a psychological tool because the same brain that goes about our daily business dreamed up the dream story. Even when people know that they've had a dream, it still seems significant to them, and it may be. Dreams reveal how our brains are processing our lives and how we feel about events.
In Genesis, Jacob saw a ladder reaching to "heaven." And then, just like Moses, he "heard" God telling him that he and his progeny would rule the earth. When he woke up he believed it was all real and he made a life-decision based on it: he "founded" the city of "Bethel." A later dream-God told him to abandon his city. This may say as much about culture as the individual: plain old good judgment can't be presumed in their leaders. They need to be supported by a higher authority.
The other big dreamer in the Bible is the most famous: Joseph, who had prophetic dreams of his own and became a dream interpreter for Pharoah. Again, assuming any of this stuff happened as it was written down hundreds or thousands of years later, this is a very convenient way for someone to manipulate another person. Just like phony psychics who do cold readings, a clever "dream interpreter" can get their mark to believe almost anything. Coincidentally, Pharoah rewarded Joseph with valuables. Joseph sounds more like a con artist to me than a prophet.
In almost every culture and in folk life generally, dream interpretation can be a game, a prophesy or a form of manipulation. Did Jacob's ladder mean anything? Did Joseph really get messages from God through his own and others' dreams?
No. Not likely at all. Dreams are just dreams, though sometimes they are revealing of something in our experience or thinking. Seeming proof of supernatural communication is wishful thinking.
Delusions
Sometimes people just seem to "know" things in the absence of having been told by a real or hallucinated figure. To the person holding the delusion it's every bit as real as the ideas they have about the actual real world. Something has gone very very wrong for them.
The obvious example from the New Testament would be Jesus, assuming he really meant "son of God" when he called himself "Son of Man." There's no description in the Bible of Jesus being told by his mother that she'd been impregnated by God. He had siblings, and presumably was the oldest, so he would have been somewhat elevated in the family by virtue just of being the oldest boy. That's enough to mess with any child's brain.
Delusional Disorder is currently defined as delusions in the absence of other symptoms, which family and culture do not support. If your culture does support the idea that a person can be magically special, it would be not be a delusion by today's standards, but I think that's a cop-out. The culture itself can share a delusion (as Richard Dawkins says of course), and an individual's psychosis can fit right in with it. More recently, we have had the famous cases of Jim Jones, Charlie Manson, and David Koresh. They were able to gather a group around themselves in a personality cult reminiscent of Jesus and his disciples, with even more success in some ways, yet would they be considered mentally ill if the outcomes hadn't been so drastic? We've been too polite about the (somewhat) less dangerous versions of them such as Mary Baker Eddy, Joseph Smith, and L. Ron Hubbard.
And the person harboring the delusion can appear normal: "Unfortunately, patients with delusional disorder do not have good insight into their pathological experiences. Interestingly, despite significant delusions, many other psychosocial abilities remain intact"
So... was Jesus really the offspring of a human-deity mating? Assuming that story wasn't cribbed from other stories current in his time, why should his belief in his divinity be more convincing than the "false" prophets? It's not.
Conclusion: Jesus, if he existed, and if his story was transmitted accurately, probably was more like Jim Jones and Charles Manson in his path to self-delusion than a truly half-divine man-god. The fact that others believed him, doesn't make it more true any more than Charlie's followers convince most of us that he was anything but a demented, delusional cult leader.
Which brings us to Paul, who in my opinion is the true inventor of Christianity. What happened to him on the road to Damascus? In Acts 9-13 it says:
As he neared Damascus on his journey, suddenly a light from heaven flashed around him. 4 He fell to the ground and heard a voice say to him, “Saul, Saul, why do you persecute me?”
5 “Who are you, Lord?” Saul asked. “I am Jesus, whom you are persecuting,” he replied. 6 “Now get up and go into the city, and you will be told what you musist do.”
7 The men traveling with Saul stood there speechless; they heard the sound but did not see anyone.
The bright light sounds hallucinatory for sure, possibly due to something like an ischemic stroke, or stress-related hallucination. This is his one big moment, not one of a long series, so he wasn't mentally ill, but he could have been in a temporarily ill state. The others "hearing the sound" doesn't necessarily confirm the experience, especially since they didn't see anyone, and presumably didn't hear the bright light. One, he was a leader and who is going to say "No, boss, I didn't hear nuthin?" But also, it's possible for the person hearing the voice to believe others also heard it. And since his companions weren't the ones writing about this story, is it likely (assuming they were real persons of course) that they were the ones telling the story to whoever did write Acts? No, it's much more likely, that if Paul existed, and if he'd heard these things, and if he told others about them, that only his version of events was written down.
So... did Paul really hear Jesus talking to him on the Road to Damascus? Since he'd never actually met Jesus before the crucifixion, how would he know? He had only the voice's word for it, and disembodied voices just can't be trusted. So my verdict on Paul: hallucination and biased reporting.
You could go through the holy stories of any other religion and find the same types of stories (sometimes the same story with different names!) and because the people telling the stories were credible, powerful, charismatic, or dishonest, the stories became the basis for religions. If you were born more than 100 years ago, you could hardly be blamed for believeng that other people's delusions, dreams, and hallucinations were actual windows into another reality.
If you believe in other people's delusions today, though, you should be ashamed of yourself.