Escargot,
The problem is that there has been plenty of substance posted on this subject in numerous threads on this board and many others. Fundies like you are too lazy to do the research that us informed folks have done. You expect us to spoon-feed you all the information, and then, when it goes against your preconceived notions of god and the universe, you decide to reject facts. But I'll play along (yet again) in the hopes that you really do want to learn something:
First of all - you implied that Neanderthals were apes because you were the one asserting that humans are not related to chimpanzees which ARE apes. One can only assume that when you put an article up showing that Neanderthals are not direct ancestors of humans that you believe them to be apes - otherwise, what was the point? Also, if you'll notice, the article you presented showed that humans and apes share a common ancestor. You have a severe reading comprehension problem if you don't understand that. Did you even read the article you posted?
Now to answer your questions:
1) Evolution is both a fact and a theory. The fossil, DNA, etc. evidence shows that all life on earth has a common origin - everything is related and has ‘progressed’ from simple to complex organisms. This is a fact. Evolution is also a theory - the theory of how this happened is Natural Selection, survival of the fittest. So evolution is both a fact and a theory. Just like gravity is a fact and a theory. It's a fact that massive bodies attract one another. Gravity is also a theory - Einstein’s is that massive bodies warp space so the shortest distance between two points isn't necessarily a straight line in 3D Euclidean space. Get the picture? Both fact and theory.
Also, try and understand the scientific usage of the word Theory. It doesn't mean "a guess" like in common usage. It means a testable framework that is used to explain facts and can make PREDICTIONS. A theory that does not make accurate predictions is not useful. Guess what? Evolution makes accurate predictions. Also, a theory must be falsifiable, otherwise it is useless. Guess what? Evolution is also falsifiable. Is your theory of special creation falsifiable? If yes, how so?
2) I'm not sure what you mean by "Explain why the “common ancestor” just can’t be right when talking evo". Humans and apes share a common ancestor. It is shown through both fossil and DNA evidence. Neanderthals are related to humans and apes, but are not our ancestors, just like your cousins are not your ancestors. Apes are not our ancestors, but are related to us like cousins as well. Apes and humans share a common ancestor millions of years ago that was not a modern ape at all. This isn't really that complicated stuff.
3) The second law of thermodynamics does not contradict evolution anymore than it contradicts the forming of snowflakes or the development of a fetus into a baby. It is true that on the whole thermodynamics means that at the end there will ultimately be entropy, but until then there are pockets of reduced entropy. This is caused by energy sources, such as the sun. If the earth was a closed system, then everything would wind down into complete entropy, but since the sun provides energy, the earth is a pocket of reduced entropy. They second law of thermodynamics has been refuted as an objection against evolution a long time ago. People who hold to this belief understand neither Evolution nor thermodynamics.
rem
"We all do no end of feeling, and we mistake it for thinking." - Mark Twain