Hello Inbetween, glad you're open to new ideas. I'll try and answer these questions, but someone else can probably add to them.
1) missing link: I do not have to go into the fossil report, what puzzles me is, that there are no missing links alive today.
Firstly, it's inescapeable that there were missing links. Fossil records prove this beyond doubt. You can study the evolution of the Horse, or the evolution of sea dwelling mammals, or even our own ancestry to get a broader picture of this. For instance, inherent in dolphins are two very small bones at the base of the spine. They are too small to have a usage, and are not connected to the rest of the skeleton, but they are the remnants of the ancient anscestors of dolphins, who originally lived on land, but over time moved out to sea (which, I might add, are visible in the fossil record).
You should also think about the term 'missing link'. If you go further forward in time, then probably every animal on the earth now would be a missing link to some new future species. But the process is so incredibly slow that we would barely notice this change. Therein lies the problem with the 'missing link' terminology. If scientists could find each and every stage of evolution in the fossil record, it would be impossible to put a defining mark between what constitutes a human, for example, and what constitutes an ape-like anscestor.
Third, when two varying branches of an individual species co-exist, one will probably go extinct. This is because of things like food competition, and struggles over territory. It's also quite probable that the Neanderthal, which was a separate branch, not related to humans, may have died out because of interbreeding with our ancestors.
2) our brain
I'm not sure whether this is more of a philosophical question than an evolutionary one. Nevertheless, our brains are capable of learning, understanding, creating and storing information. Because of this we are able to create a necessity for answers to questions like 'Is there a God' and 'Why are we here'. It is our brains that give the universe purpose. But truth is objective. There are some things that we can find the answers to, and that's where science comes in.