Science is the search for natural explinations to observed phenomina. This is the description accepted by National Academy of Sciences, and most scientists in general. Your allusion to prediction has to do with a statement to be considered scientific it must make a statement about the world that can be proven untrue. Not that it is untrue, but that you can think of an example that would show the statement is untue. If the example that denies the statement does not infact exist in the real world, then the scientific staement is accepted as provisionally correct.
These statements about the world are then generalized, if possible, and combined into a theory. If an example of irreduable complexity could be produced, then the theory of evolution would have a problem. The supposition has been valuable because what opponants of evolution have called irreducibly complex have often pointed to gaps in our understanding. When actually subjected to investigation, the examples have been shown not to be irreducibly complex. The example from the Dover case was the imune system which in the last decade has actually yeilded up much of its secrets, which are helping us understand imune disorders and cure diseases, while calling it irreducibly complex and was therfore made by a designer hasn't helped understand anything, and certainly would never move us closer to understanding diseases like lupus and MS.
Evidence of ignorance is only evidence of ignorance (refering to lack of understanding among scientists, and not an insult to you). Evidence of ignorance is not evidence of a creator, a designer, or a flying spagetti monster. Should schools teach about these gaps in knowledge? Absolutly, one of the kids in a biology class might want to know what is in that gap and go to college and discover the answer. Or not discover the answer but instead become very interested in dolphins and decipher what it is they are saying. Personally I think dolphins are talking about how great fish taste and how much fun sex is, because they live in the water, what else are they going to talk about?
I think a ninteen year old and a thirteen year old could cary on quite complete conversations on topics like football plays, which can be very complex. Dirty jokes, which often have all sorts of subtext. Perspective and optics should be within the grasp of a thirteen year old. The ninteen year old has more knowledge, so would be the role of educator, but the thirteen year old should be able to follow the argument. As for emotionally, the thirteen year old will be basing their own future behavior on what the ninteen year old tells them. If they haven't had their first crush, they aren't going to understand the feeling, of course. But you don't need empathy or emotional maturity to understand science or mathematics, you just need some one to explain it to you and answer your questions.