"However, I do not think Darwinism is up to snuff with scientific standards. For a scientific theory to be credible, it needs to yield results that are reproducible. It needs to predict what will happen and be right. The theory of gravity predicts that an object will accelerate at a rate of 9.8 meters per second per second when dropped anywhere on earth."
The theory of evolution predicts that the organisms best suited to reproduce in their environment will reproduce and pass on their traits to offspring. It's an explanation of how we got to where we are, and while it doesn't give you an exact formula where you can plug in variables like gene drift, population density, breeding patterns, etc., it is a marvelous explanatory tool. Evolution is emphatically NOT equivalent to chance.
"Sexuality is wholly unproductive. To require another organism to procreate is a great hindrance. It is much more successful to reproduce asexually. Yet Most multicellular organism are sexual organisms. This does not hold for Darwin's theory."
This is an astute observation. It's a difficult thing to explain and it's something that scientists have been working towards for some time. One big benefit to sex is recombination. You might not pass on ALL (and in a few generations it's entirely possible you'll pass on none) of your genes, but for the immediate future you might also pass on the good ones and get rid of the bad ones. Sex gives you a true gene pool, it allows for mutations in the population to correct themselves, and that in some sense channels the direction of evolution. It also selects for genes that "co-operate" well. Genes that don't like working with certain other genes get selected out, leading to rather harmonious individual bodies. At any rate, I can't do the debate justice, look into George C. Williams' book Sex and Evolution, Graham Bell's The Masterpiece of Nature, or Matt Ridley's The Red Queen (good for non-specialists).
Homosexual behavior can be explained with numerous hypotheses: Homosexual members of a community don't reproduce, and so can help to raise their nieces and nephews, which share ~25% of their genes. As far as your quarrel with it being passed on, it's as much a product of environmental factors in the womb as it is of genes. Even were it entirely genetic, it's not like that would preclude a stable allele ratio. Sexuality isn't black and white, homosexual and heterosexual, it's more of a continuum. Some people are attracted to both sexes, or one sex somewhat more than the other or somewhat less, or to neither sex at all. It's also worth noting that species like bonobos who "build their society around homosexual behavior," use sexual favors as a way to establish social hierarchies. It's not like they don't have heterosexual sex when they feel like it, they just don't discriminate that much because to do so would be socially isolating.
Your assertion about proteins: Genes code for proteins. Proteins are ultimately the products of genes. Are you talking about epigenetics?
As far as rape as a successful reproductive strategy: For some species it is. But other species figured out ways to avert such situations, and genetically pressured such mating behavior out of existence. As species became genera became families became orders etc, the traits passed down. Sometimes they reverted, sure but it's not that hard to conceive.
For intermediates: This is a problem that Richard Dawkins has called the Fallacy of the Discontinuous Mind. Categorization is /what humans do/. Our ancestors were selected to discriminate quickly between various objects. Evolution /is/ a continuous process. There is no point in evolutionary history where it is perfectly clear that a bird stopped being a dinosaur. But dinosaurs became more birdlike. Hominins became more like Homo sapiens. To give an example of continuity geographically (which is more or less identical to temporal variation), there's a population of salamanders that live along the west coast of North America. Around California's Central Valley there's a ring of salamanders with a break at the southern extremity. on the southwest end of the ring the salamanders are more or less brown. Further north they get little yellow stipples. Further north the stipples turn into dots, which get more and more pronounced as you go around the ring and eventually turn into stripes. Now, the salamanders at either end of the ring (and say, just to say, every 1/8th of the way along the ring) won't breed with each other. But if you take two salamanders separated by five miles along this continuum you'll have a string of salamanders about double the length of California that will breed with some number of their neighbors until they discriminate the potential partner as an ineligible mate. If you went back 1000 years, picked up a male human, took him back 1000 years, picked up a female human, they could breed. Go another 1000 years back, pick up a male. He can breed with the woman. Another thousand years and a woman could still breed with the male. You could do this all the way to the evolution of distinct sexes, picking up individuals of alternating sexes at 1000 year intervals. There's no distinct point at which a species is "official" in the temporal dimension. At any rate, there is no lack of intermediate fossils. There is rather a great abundance of them. The problem is that whenever one is found, people like you say "Oh, now you've got /two/ gaps to fill." Regardless, even in the entire absence of fossils molecular evidence from DNA shows a common heritage of all life on earth.
As far as your questions about why there aren't multiple species on earth with human levels of cognition, the answer is that it can't just come from nowhere. If there's no evolutionary pressure for larger brains and better problem solving or social skills, then organisms aren't going to waste resources on extravagant cognition machines that could be better spent on reproduction or muscular development or whatever. Evolution doesn't leap up a cliff, it slowly climbs up a very shallow slope.