I've been doing some research about evolution and I'm having a few doubts, would love for someone here to clear them up.
1) Addition of information to the genome. How could it be that the Homo Erectus who had a brain size about half our size had their brain size doubled in us, with billions of extra neurons added? Could a single mutation of the DNA be enough for such a large change to occur?
No. multiple mutations over a long time. Brain went from 400 cc to about (1100cc?) over a long time. Elephants since 1925 had been growing smaller and smaller tusks, till now we have elephants that grow no tusks whatsoever. After a while, we will get more an more elephants that will grow no tusks. Once people stop killing them for tusks, it is highly probably that the elephants will grow their tusks again, unless too much time has passed with the elephants growing no tusks.
Secondly, what about the new features added to an organism, like the ability of the human eye to see colors, the wings added to the birds, etc? Where does the knowledge to create these new organs come from?
Knowledge is not the correct word. But let's use it for the purpose of this. Most of the knowledge comes from past DNA in the species.
Certain traits have a range. Some do not. Skin can have a range of colors. Can have a range of patterns like small dots and large dots. Size is another one that often falls in a range. Somehow, the inside of our organs is almost always the same color. Livers look the same. There just was no purpose for livers to change colors.
So experiments tells us that, for a fish that has dots on its skin. If the fish was to have its offpsring split, some placed with big rocks, some placed with small rocks, then 99.99% of the offspring, will either develop big dots to adapt to big rocks, or small dots to adapt to small rocks. But it would be unknown and unpredictable, if, and when, any will develop something completely new like 'bony ridges' to mimic stones, or even the ability to lick extra food from the stones. The last Two traits might, or might not happen. Even if beneficial to the fish, it still might or might not happen. No guarantees on new features. Only guarantee on existing features.
2) My understanding is that a random mutation causes a change in a species to occur, and then natural selection helps spreading this change out and eventually speciation occurs where the ancestor species and the new species can no longer reproduce.
yes. natural selection = manual selection in the case of breeding, sexual selection, survival selection and the other types of selection.
How could random mutations have been so successful to consistently produce the various very complex traits found in the species? E.g wings, long neck of the giraffe, stripes of the zebra, claws and the strength of lions & tigers which make them more effective than smaller cats, etc?
Because we observed small changes in the lab from one parent to its kids. Certain traits were already programmed in the specie, but every now and then, something new and completely novel takes hold. Generally speaking though, random mutations causes death and disabilities.
3) How did random mutations helped in the evolution from the earliest bi-polar apes (e.g Lucy) to homo erectus, to human beings, etc? Was it just random mutations that caused homo erectus to lose their body hair, or was there a controlled process behind it which knew that less hair would be more beneficial? Please clarify.
Your Second point answered this question. Mutation is random, Natural selection is not. Natural selection is a very cruel picker as well.