Fair enough, Naomi, it'll take some time to address each of Matheous' questions though. A lot of them appear to me to be misconceptions, though.
Most of your weird effects appear in Quantum Mechanics but this is a "nonrelativistic" theory -- that is, that don't fully describe what is going on because they ignore (special) relativity. Some of the weird effects are then similar to what you get in even Newton's theory of gravity. This has everything connected to everything else, everywhere, instantaneously -- so, if the Sun disappeared right now, according to Newton's theory the Earth would instantly respond. Indeed, we would also instantly notice if the galaxy Andromeda vanished, subtle changes in the gravity field occurring even as we could see the galaxy still there. But this is presumed to be a nonsense, as information is held to travel at no faster than the speed of light -- related to the "Principle of Causality". There's no proof that this is so, it's an assumption, but it does fit with all known experimental data so far.
In the same way, many of the weird effects of Quantum Mechanics are related to the fact that the theory in which these effects appear is incomplete. This is not to say that those stories are wrong -- it's just that you should be careful of the interpretation. That said, things are probably weirder in the full theory. Anyway...
"Who can believe that one thing can exist in two places at the same time?"
Presumably you are referring to the double-slit experiment, an electron particle interfering with itself as it passes through both slits at once? Thing is, that it was never just in one place to start with. I don't know quite how to continue that thought, but... the basic gist is that until you have observed the particle it could be anywhere (with varying degrees of probability for each location), and even on observing it there is an uncertainty in the position.
Also it's a matter of interpretation. The "truth", if there is such a thing, is that we try to make pictures out of what the mathematical equations tell us. All of those pictures are wrong, some are more wrong than others. For myself, I have great difficulty in this "it's a particle when you are looking at it" idea, because a particle is a crude approximation itself. Better to think of the electron as a wave, whose behaviour obeys the laws of quantum probability, but whose wave-like properties can be ignored in certain cases.
I don't know if this is the main-line interpretation, but it neatly sidesteps all apparent paradoxes that I know of, and also seems to be as close to the truth as possible. We don't know what an electron is. We do know how to describe it, to varying degrees of accuracy. At the level of the Schrodinger equation, the picture allows you to talk of the particle as if it is in two places at once, but then it's only a picture.
"Who can accept that something can change a particle at potentially an immense distance and do so 'instantly'? Also faster than light!"
The EPR Paradox, two particles that are part of the same system seemingly connected across any distance, instantly. The connection is real, the phenomenon has been observed, but it's not clear that any information travels faster than light. Suppose you have two particles, A and B, coupled together in this way, and you send B off to Mars where someone is waiting for it. Then look at A, and this will change the state of B too. But the person on Mars, looking at B, has no way of determining whether or not you looked at A. No information moves between the two places, but the result of B's experiment can be known before he performs it -- but not by the person himself. Neither do the experimenters have any control over the outcome, so there is no way for either person to tell if the other person has performed the experiment before he can find out by "at-light-speed" means. Again, care is needed in interpreting what is going on.
More to follow as I've run out of characters.