And the people who are shown and do see and hear God, is it true for them? Do they "need" to prove it, or even say anything about what they "see" and "hear"? You may or may not realise that I am not referring to seeing with eyes, or hearing with ears--it's just a convenient terminology, the experience is beyond description, in actuality.
Does that mean someone who experiences nirvana, and never says a word about it (because they also realise it can't be described) is not being "scientific" and making a testable prediction?
It depends upon the claims being made. Science is just a methodology for examining the physical world. It depends upon certain conditions (primarily testability) that are not available for all phenomena.
So the question becomes, are the claims being made testable? If they are, then they fall under the purview of science. So if someone states, for example, that faith healing is true we can examine that claim. For subjective experiences, not so much. There's really no way to test someone's experience of Nirvana or God, or the lack thereof. Which is fine, we have to allow for those differences. We can debate them and analyze the rational of their interpretation, but ultimately they belong wholly to the person who has them.
The problem I find is that people who have such experiences rarely stay within these limitations. They set off making claims they cannot substantiate and tend to get rather upset when the claims are examined.
I can make a personal analogy. I have color deficient vision. So from a very young age I realized that the world I see was not the same world other people see. In a sense, I am inherently "atheistic" about certain shades of green (they appear grey to me). Yet lots of people tell me that these shades to exist. How am I to know whether they do or not? Well, the simplest method is to analyze the claims. If one person tells me that a particular object is green I can go ask another person to see if they agree. The more congruent the answers, the more likely they are to be accurate.
Yet, when you start testing people about god, there is very little in the way of congruence. If we start redefining god in the most basic and general concepts that are common to the perception you will find they become very vague indeed. In general terms your definition is spot on, "that which is beyond the understanding" or a sense of unity. But anything then said beyond this is not about god. Rather it is a reflection of the psychology of those making the statements. If you examine the statements you'll find strong support for this. They are almost entirely emotive.
Well, what is anyone talking about when they talk about their existence? Is "existence" laden with superstition and myth?
I don't find that term particularly problematic. Certainly the idea of what existence is can be loaded with superstition and myth but it's relatively simple to strip it down to its essentials. I don't find this true of the term "god".
Let's see: humans often define themselves as superior to all other animals, but isn't that based on a myth, or even a self-delusion? Obviously humans are also animals.
It depends on how you define "superiority". It's a value based determination so it does indeed seem rather self serving to judge all animals by human standards. Humans don't make very good toads and probably wouldn't fare well in judgment if toads had a value system.
There are humans who define their existence, and what they have to say about it, as being more "important" than that of other humans, often by describing others as "less" than human--there is apartheit, racism, religious intolerance, elitism etc. Humans are beset by myth and superstition when they confront the question of their own existence.
All the more reason to reach outside our subjective experiences. These things don't hold up under broader examination.
~Raithere