Some of your questions are so very basic that you really should be consulting a book or introductory website instead of coming here and asking us to teach all this to you. I'll address some of your points. I recommend you check out talkorigins.org and also perhaps pick up a copy of Richard Dawkins' book The Greatest Show on Earth.
1 Apes still exist because they evolved in to the species of ape that they evolved in to, and we evolved into the species of ape that we evolved in to. The purpose of evolution is not to make people. Also, many modern organisms are similar to many prehistoric ones that other organisms evolved from. For example, the evolutionary history of modern humans includes primitive single-celled organisms, primitive chordates, fish, amphibians, reptiles, and other mammals and yet animals that would be classified in these categories still exist today.
a. Some probable human ancestors include those shown here: http://www.talkorigins.org/faqs/comdesc/hominids.html
Their names are listed at the bottom.
b. Skin color is an adaptation to environment. Most early human ancestors would have had dark skin as they had adapted to the harsh African sun. When we moved into Europe and other climates the increased levels of melanin in our skin hindered the production of vitamin D because the sunlight was much less intense. Lighter skin was an adaptation of this.
i. Humans are different species from the non-humans we evolved from. I'm not sure what you mean by "different within ourselves" If a group of humans became isolated from the rest of us for a million years it is possible that over such a long period of time they could evolve into something we would consider non-human.
ii. I believe I already addressed this above.
c. You really should have done at least a few minutes of research before asking this. When organisms reproduce the DNA is copied. During this process, subtle mutations in the DNA can be introduced that manifest as slightly different physical traits in the offspring. This is why all people don't look alike. In the wild, these traits can benefit the survival of the organism or hinder it. Traits that increase survivability will increase in a population since those organisms will be more likely to reproduce and pass the trait to their offspring. These subtle changes accumulate over time possibly leading to a very different organism than the one you started with.
i. the genetic mutations occur because biological processes aren't perfect. Exposure to ultraviolet light, nuclear radiation, and certain chemicals can damage DNA also.
ii. When an animal is very suited to it's environment, new traits may be more likely to hinder that animals ability to survive. If an animal is not suited to its environment, then new traits may be necessary. Other apes have been evolving for just as long as we have, but we seem to have undergone more drastic changes and this was probably out of necessity for survival in the unsuitable environment we found ourselves in. That is why the ancestors in our lineage were "selected"
2. I would say because despite our advanced intelligence we still unfortunately retain remnants of our evolutionary past which causes us to desire to obtain and defend territory and to fear things that are unknown. We are driven by the same base, primitive instincts that our primitive ancestors were. We still have a long way to go to become totally rational beings.
a. I have no idea what you mean here.
b. the differences in race are the result of those changes and adaptions that cause evolution. Different populations of humans used to be mostly isolated from other populations. Different traits emerged and accumulated in certain populations causing the subtle variations of different races that we see today.
"I'd like a Atheist to answer these questions. Truth is, you can't. Simply because we never evolved from Apes to begin with."
As I have shown you are clearly wrong. Science has been studying evolution for 150 years and we have mountains of evidence supporting it. We have dinosaurs with feathers and fish with feet. We've mapped the genome of humans and chimps and they are 96% identical. There have been numerous hominid fossil discoveries. We even have fossils that show the migration of the blow hole up to the top of the head in modern whales and of the development of the horse hoof. Genetic mutations have been observed. Natural selection has been observed.
Evolution, based on all current available information, is a fact.