Obviously false. Look: I brushed my teeth this morning. That's my claim. Are you saying I should be regarded as telling a falsehood unless I can demonstrate that I brushed my teeth this morning? I obviously cannot do that (I didn't take any selfies in the process or anything, and my wife was downstairs so there were no witnesses). But in fact, my claim is true, and any number of other true claims are in the same situation. For example, I also rinsed with mouthwash. The problem with your standard is that if we adopt it, we will end up regarding as untrue a great many claims that are, in fact, true.
Again, clearly false. Suppose someone makes a profile on this site and makes exactly one post, and then never posts again. Should we think their post is mere statistical fluke? Seems to me we should assume someone-some human being-made exactly one post.
Now, let me offer a diagnosis: it depends on what makes us think it's a signal from outer space. If the signal lasts, say, eight hours, and is formatted so as to transmit images of math worked out in arabic numerals, giving us solutions to problems no human being could offer, that wouldn't be a statistical fluke. The lesson is that the content of the signal matters. Similarly, by analogy, the content of an experience matters.
Again, false. I take it everyone knows that breaking a finger is a painful experience. But if I break my finger, you cannot examine my pain. By your principle, since no one else can examine my pain, no one should believe I'm actually in pain. And so for all experiences that every person has, day-in, day-out.
I'm not sure what you mean.